Supersymmetry and non-commutative geometry

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Supersymmetry and non-commutative geometry

  1. 1. & SUPERSYMMETRY NONCOMMUTATIVE  GEOMETRY Thijs  van  den  Broek Workshop  Bayrischzell Radboud  Univ.  Nijmegen  /  NIKHEF May  22nd,  2011Wednesday, May 30, 2012
  2. 2. Wednesday, May 30, 2012 Intro INTRODUCTION
  3. 3. The  project Approach ApplicaNon Preliminary  results Outlook The  research  project Joint  work  with  Walter  van  Suijlekom  and  Wim  Beenakker Try  to  extend  the  Standard  Model  from  NCG  with  supersymmetry   (Everywhere:  N=1  supersymmetry  ,  i.e.  MSSM) Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  4. 4. The  project Approach ApplicaNon Preliminary  results Outlook The  research  project Joint  work  with  Walter  van  Suijlekom  and  Wim  Beenakker Try  to  extend  the  Standard  Model  from  NCG  with  supersymmetry   (Everywhere:  N=1  supersymmetry  ,  i.e.  MSSM) How  supersymmetric  is  the  resulNng  acNon? (So:  no  superfields  or  anything...) Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  5. 5. The  project Approach ApplicaNon Preliminary  results Outlook The  research  project Joint  work  with  Walter  van  Suijlekom  and  Wim  Beenakker Try  to  extend  the  Standard  Model  from  NCG  with  supersymmetry   (Everywhere:  N=1  supersymmetry  ,  i.e.  MSSM) How  supersymmetric  is  the  resulNng  acNon? (So:  no  superfields  or  anything...) Does  it  share  the  merits  of  ‘ordinary’  supersymmetry? (E.g.  hierarchy  problem) Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  6. 6. The  project Approach ApplicaNon Preliminary  results Outlook The  research  project Joint  work  with  Walter  van  Suijlekom  and  Wim  Beenakker Try  to  extend  the  Standard  Model  from  NCG  with  supersymmetry   (Everywhere:  N=1  supersymmetry  ,  i.e.  MSSM) How  supersymmetric  is  the  resulNng  acNon? (So:  no  superfields  or  anything...) Does  it  share  the  merits  of  ‘ordinary’  supersymmetry? (E.g.  hierarchy  problem) Can  we  predict  anything  from  this? (E.g.  scalar  masses,  c.f  Higgs  mass) Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  7. 7. The  project Approach ApplicaNon Preliminary  results Outlook The  research  project Joint  work  with  Walter  van  Suijlekom  and  Wim  Beenakker Try  to  extend  the  Standard  Model  from  NCG  with  supersymmetry   (Everywhere:  N=1  supersymmetry  ,  i.e.  MSSM) How  supersymmetric  is  the  resulNng  acNon? (So:  no  superfields  or  anything...) Does  it  share  the  merits  of  ‘ordinary’  supersymmetry? (E.g.  hierarchy  problem) Can  we  predict  anything  from  this? (E.g.  scalar  masses,  c.f  Higgs  mass) Why  want  this? Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  8. 8. The  project Approach ApplicaNon Preliminary  results Outlook The  research  project Joint  work  with  Walter  van  Suijlekom  and  Wim  Beenakker Try  to  extend  the  Standard  Model  from  NCG  with  supersymmetry   (Everywhere:  N=1  supersymmetry  ,  i.e.  MSSM) Why  want  this? Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  9. 9. The  project Approach ApplicaNon Preliminary  results Outlook The  research  project Joint  work  with  Walter  van  Suijlekom  and  Wim  Beenakker Try  to  extend  the  Standard  Model  from  NCG  with  supersymmetry   (Everywhere:  N=1  supersymmetry  ,  i.e.  MSSM) Why  want  this? Promising  BSM  candidate. Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  10. 10. The  project Approach ApplicaNon Preliminary  results Outlook The  research  project Joint  work  with  Walter  van  Suijlekom  and  Wim  Beenakker Try  to  extend  the  Standard  Model  from  NCG  with  supersymmetry   (Everywhere:  N=1  supersymmetry  ,  i.e.  MSSM) Why  want  this? Promising  BSM  candidate. To  see  what  NCG  might  have  in  store  for  us.   Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  11. 11. The  project Approach ApplicaNon Preliminary  results Outlook The  research  project Joint  work  with  Walter  van  Suijlekom  and  Wim  Beenakker Try  to  extend  the  Standard  Model  from  NCG  with  supersymmetry   (Everywhere:  N=1  supersymmetry  ,  i.e.  MSSM) Why  want  this? Promising  BSM  candidate. To  see  what  NCG  might  have  in  store  for  us.   UnificaNon  of  coupling  constants: vs Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  12. 12. The  project Approach ApplicaNon Preliminary  results Outlook MoNvaNng  example:  super-­‐QCD  [1]  (1/2) Take:   tensored  with where parametrizing  a  3-­‐tuple and  its  conjugate. 1TvdB, W. D. van Suijlekom, Physics Letters B 699 (2011), 119–122 Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  13. 13. The  project Approach ApplicaNon Preliminary  results Outlook MoNvaNng  example:  super-­‐QCD  [1]  (1/2) Take:   tensored  with where ‘quark’ ‘anNquark’ ‘gluino’ parametrizing  a  3-­‐tuple and  its  conjugate. 1TvdB, W. D. van Suijlekom, Physics Letters B 699 (2011), 119–122 Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  14. 14. The  project Approach ApplicaNon Preliminary  results Outlook MoNvaNng  example:  super-­‐QCD  [1]  (2/2) Inner  fluctuaNons   parametrize  (anN)squark 1TvdB, W. D. van Suijlekom, Physics Letters B 699 (2011), 119–122 Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  15. 15. The  project Approach ApplicaNon Preliminary  results Outlook MoNvaNng  example:  super-­‐QCD  [1]  (2/2) Inner  fluctuaNons   parametrize  (anN)squark Gauge  group                              :  superpartners 1TvdB, W. D. van Suijlekom, Physics Letters B 699 (2011), 119–122 Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  16. 16. The  project Approach ApplicaNon Preliminary  results Outlook MoNvaNng  example:  super-­‐QCD  [1]  (2/2) Inner  fluctuaNons   parametrize  (anN)squark Gauge  group                              :  superpartners Spectral  acNon                                                ,  extra  terms: Inner  product: 1TvdB, W. D. van Suijlekom, Physics Letters B 699 (2011), 119–122 Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  17. 17. The  project Approach ApplicaNon Preliminary  results Outlook MoNvaNng  example:  super-­‐QCD  [1]  (2/2) Inner  fluctuaNons   parametrize  (anN)squark Gauge  group                              :  superpartners Spectral  acNon                                                ,  extra  terms: Inner  product: SUSY  automaNcally  broken:  (minus)  mass  terms  for  squarks. 1TvdB, W. D. van Suijlekom, Physics Letters B 699 (2011), 119–122 Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  18. 18. Wednesday, May 30, 2012 APP APPROACH
  19. 19. The  project Approach ApplicaNon Preliminary  results Outlook The  approach Problem: More  realisNc  situaNons:  calculaNons  get  out  of  hand More  systemaNcal  approach  needed  (cf.  superfields) Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  20. 20. The  project Approach ApplicaNon Preliminary  results Outlook The  approach Problem: More  realisNc  situaNons:  calculaNons  get  out  of  hand More  systemaNcal  approach  needed  (cf.  superfields) Plan: 1)  Define  ‘supersymmetric  spectral  triple‘     2)  Prove  ‘susy  spectral  triple’ supersymmetric  acNon spectral  acNon 3)  MSSM  as  a  special  case Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  21. 21. The  project Approach ApplicaNon Preliminary  results Outlook Intermezzo:  Krajewski  diagrams Finite  spectral  triple:   Krajewski  diagram: Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  22. 22. The  project Approach ApplicaNon Preliminary  results Outlook Intermezzo:  Krajewski  diagrams Finite  spectral  triple:     Krajewski  diagram: Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  23. 23. The  project Approach ApplicaNon Preliminary  results Outlook Intermezzo:  Krajewski  diagrams Finite  spectral  triple:     Krajewski  diagram: ... ... ... ... Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  24. 24. The  project Approach ApplicaNon Preliminary  results Outlook Intermezzo:  Krajewski  diagrams Finite  spectral  triple:       Krajewski  diagram: ... ... ... ... Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  25. 25. The  project Approach ApplicaNon Preliminary  results Outlook Intermezzo:  Krajewski  diagrams Finite  spectral  triple:       Krajewski  diagram: ... ... ... ... Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  26. 26. The  project Approach ApplicaNon Preliminary  results Outlook Intermezzo:  Krajewski  diagrams Finite  spectral  triple:       Grading Krajewski  diagram: ... ... ... ... Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  27. 27. The  project Approach ApplicaNon Preliminary  results Outlook Intermezzo:  Krajewski  diagrams Finite  spectral  triple:       Grading Krajewski  diagram: ... ... ... ... Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  28. 28. The  project Approach ApplicaNon Preliminary  results Outlook Intermezzo:  Krajewski  diagrams Finite  spectral  triple:       Grading Dirac  operator     Krajewski  diagram: ... ... ... ... Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  29. 29. The  project Approach ApplicaNon Preliminary  results Outlook Intermezzo:  Krajewski  diagrams Finite  spectral  triple:       Grading Dirac  operator     Krajewski  diagram: ... ... ... ... Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  30. 30. The  project Approach ApplicaNon Preliminary  results Outlook Intermezzo:  Krajewski  diagrams Finite  spectral  triple:       Grading Dirac  operator       Krajewski  diagram: ... ... ... ... Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  31. 31. The  project Approach ApplicaNon Preliminary  results Outlook Intermezzo:  Krajewski  diagrams Finite  spectral  triple:       Grading Dirac  operator       Krajewski  diagram: ... ... ... ... Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  32. 32. The  project Approach ApplicaNon Preliminary  results Outlook Intermezzo:  Krajewski  diagrams Finite  spectral  triple:       Grading Dirac  operator     ‘KO-­‐dimension’   Krajewski  diagram: ... ... ... ... Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  33. 33. The  project Approach ApplicaNon Preliminary  results Outlook Superpartners  (1/2) General  scheme  as  in  super-­‐QCD: ParIcle Superpartner fermions:   sfermions:   Hilbert  space finite  Dirac  operator gauge  bosons:   gauginos:   Dirac  operator  on Hilbert  space  (adjoint  reps.) Higgs:   Higgsinos:   finite  Dirac  operator Hilbert  space Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  34. 34. The  project Approach ApplicaNon Preliminary  results Outlook Superpartners  (2/2) Gauge  group: : ParIcle Superpartner fermions:   sfermions:   Hilbert  space finite  Dirac  operator gauge  bosons:   gauginos:   Dirac  operator  on Hilbert  space  (adjoint  reps.) Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  35. 35. The  project Approach ApplicaNon Preliminary  results Outlook Superpartners  (2/2) Gauge  group: : ParIcle Superpartner fermions:   sfermions:   Hilbert  space finite  Dirac  operator gauge  bosons:   gauginos:   Dirac  operator  on Hilbert  space  (adjoint  reps.) Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  36. 36. The  project Approach ApplicaNon Preliminary  results Outlook Superpartners  (2/2) Gauge  group: : ParIcle Superpartner fermions:   sfermions:   Hilbert  space finite  Dirac  operator gauge  bosons:   gauginos:   Dirac  operator  on Hilbert  space  (adjoint  reps.) Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  37. 37. The  project Approach ApplicaNon Preliminary  results Outlook Superpartners  (2/2) Gauge  group: : ParIcle Superpartner fermions:   sfermions:   Hilbert  space finite  Dirac  operator gauge  bosons:   gauginos:   Dirac  operator  on Hilbert  space  (adjoint  reps.) Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  38. 38. The  project Approach ApplicaNon Preliminary  results Outlook Superpartners  (2/2) Gauge  group: : ParIcle Superpartner fermions:   sfermions:   Hilbert  space finite  Dirac  operator gauge  bosons:   gauginos:   Dirac  operator  on Hilbert  space  (adjoint  reps.) Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  39. 39. The  project Approach ApplicaNon Preliminary  results Outlook R-­‐parity  &  KO-­‐dimension  (1/2) Problem the  gaugino-­‐sector  (adjoint  elements  of                )   incompaNble  with                                             Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  40. 40. The  project Approach ApplicaNon Preliminary  results Outlook R-­‐parity  &  KO-­‐dimension  (1/2) Problem the  gaugino-­‐sector  (adjoint  elements  of                )   incompaNble  with                                             In  fact parts  of  finite  spectral  triple  possibly  of  different  KO-­‐ dimensions Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  41. 41. The  project Approach ApplicaNon Preliminary  results Outlook R-­‐parity  &  KO-­‐dimension  (1/2) Problem the  gaugino-­‐sector  (adjoint  elements  of                )   incompaNble  with                                             In  fact parts  of  finite  spectral  triple  possibly  of  different  KO-­‐ dimensions SoluNon given:   two  spectral  triples   of  KO-­‐dimension                            (say)   an  operator            with: Direct  sum: Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  42. 42. The  project Approach ApplicaNon Preliminary  results Outlook R-­‐parity  &  KO-­‐dimension  (2/2) Direct  sum: Use            to  ‘even  out’  the  KO  dimensions: three  new  signs (‘super-­‐KO-­‐dimension’?) Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  43. 43. The  project Approach ApplicaNon Preliminary  results Outlook R-­‐parity  &  KO-­‐dimension  (2/2) Direct  sum: Use            to  ‘even  out’  the  KO  dimensions: three  new  signs (‘super-­‐KO-­‐dimension’?) Example KO-­‐dimensions  6  (SM)  and  0  (gauginos)  has: i.e. Role ‘R-­‐parity’,  where Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  44. 44. The  project Approach ApplicaNon Preliminary  results Outlook A  supersymmetric  spectral  triple DefiniNon We  call  an  R-­‐parity  extended  spectral  triple: a  spectral  triple   that  is  extended  with  a  grading saNsfying: such  that where with  only We  write: Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  45. 45. The  project Approach ApplicaNon Preliminary  results Outlook A  supersymmetric  spectral  triple DefiniNon We  call  an  R-­‐parity  extended  spectral  triple: a  spectral  triple   that  is  extended  with  a  grading saNsfying: such  that (...) DefiniNon An  R-­‐parity  extended  spectral  triple  is  supersymmetric  when: each  element  that  transforms  under  the  gauge  group comes  in  both          -­‐values.   all  allowed  components  of  the                -­‐  part  of  the  Dirac  operator   are  nonzero. Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  46. 46. The  project Approach ApplicaNon Preliminary  results Outlook A  supersymmetric  spectral  triple DefiniNon We  call  an  R-­‐parity  extended  spectral  triple: a  spectral  triple   that  is  extended  with  a  grading saNsfying: such  that (...) DefiniNon An  R-­‐parity  extended  spectral  triple  is  supersymmetric  when: each  element  that  transforms  under  the  gauge  group comes  in  both          -­‐values.   all  allowed  components  of  the                -­‐  part  of  the  Dirac  operator   are  nonzero. Hope  (sNll) The  acNon  resulNng  from  such  a  spectral  triple  (via  the  spectral   acNon  principle)  is  automaNcally  supersymmetric. Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  47. 47. Wednesday, May 30, 2012 APP APPLICATION
  48. 48. The  project Approach ApplicaIon Preliminary  results Outlook Why  the  SM? A  nice  way  to  look  at  things  is  provided  by  Chamseddine  &  Connes  [2]: Look  for  irreducible  soluNons   of  a  pair                                  :               Chamseddine  &  Connes,  Why  the  Standard  Model,  0706.3688v1  [hep-­‐th] Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  49. 49. The  project Approach ApplicaIon Preliminary  results Outlook Why  the  SM? A  nice  way  to  look  at  things  is  provided  by  Chamseddine  &  Connes  [2]: Look  for  irreducible  soluNons   of  a  pair                                  :               Either: acNng  on with Chamseddine  &  Connes,  Why  the  Standard  Model,  0706.3688v1  [hep-­‐th] Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  50. 50. The  project Approach ApplicaIon Preliminary  results Outlook Why  the  SM? A  nice  way  to  look  at  things  is  provided  by  Chamseddine  &  Connes  [2]: Look  for  irreducible  soluNons   of  a  pair                                  :               Either: acNng  on with Or: acNng  on with Chamseddine  &  Connes,  Why  the  Standard  Model,  0706.3688v1  [hep-­‐th] Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  51. 51. The  project Approach ApplicaIon Preliminary  results Outlook Why  the  SM? A  nice  way  to  look  at  things  is  provided  by  Chamseddine  &  Connes  [2]: Look  for  irreducible  soluNons   of  a  pair                                  :               Either: acNng  on with IncompaNble  with Or: acNng  on with Chamseddine  &  Connes,  Why  the  Standard  Model,  0706.3688v1  [hep-­‐th] Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  52. 52. The  project Approach ApplicaIon Preliminary  results Outlook Why  the  SM? A  nice  way  to  look  at  things  is  provided  by  Chamseddine  &  Connes  [2]: Look  for  irreducible  soluNons   of  a  pair                                  :               Either: acNng  on with IncompaNble  with Or: acNng  on with Chamseddine  &  Connes,  Why  the  Standard  Model,  0706.3688v1  [hep-­‐th] Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  53. 53. The  project Approach ApplicaIon Preliminary  results Outlook Why  the  SM Why  the  MSSM ObservaNon: Given  the  soluNon                                                                                                    for  the  algebra  we  we  can  take  not   only                                                                                                      but  in  addiNon  to  that  also  the  soluNon                                                                                            for  each  of  the  two  components  of  the  algebra: with Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  54. 54. The  project Approach ApplicaIon Preliminary  results Outlook Why  the  SM Why  the  MSSM ObservaNon: Given  the  soluNon                                                                                                    for  the  algebra  we  we  can  take  not   only                                                                                                      but  in  addiNon  to  that  also  the  soluNon                                                                                            for  each  of  the  two  components  of  the  algebra: with There  is  an  R-­‐parity  operator: (From                                                                                                                                                    ) Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  55. 55. The  project Approach ApplicaIon Preliminary  results Outlook Why  the  SM Why  the  MSSM ObservaNon: Given  the  soluNon                                                                                                    for  the  algebra  we  we  can  take  not   only                                                                                                      but  in  addiNon  to  that  also  the  soluNon                                                                                            for  each  of  the  two  components  of  the  algebra: with SM  parNcles There  is  an  R-­‐parity  operator: (From                                                                                                                                                    ) Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  56. 56. The  project Approach ApplicaIon Preliminary  results Outlook Why  the  SM Why  the  MSSM ObservaNon: Given  the  soluNon                                                                                                    for  the  algebra  we  we  can  take  not   only                                                                                                      but  in  addiNon  to  that  also  the  soluNon                                                                                            for  each  of  the  two  components  of  the  algebra: with SM  parNcles “Gaugino’s” There  is  an  R-­‐parity  operator: (From                                                                                                                                                    ) Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  57. 57. The  project Approach ApplicaIon Preliminary  results Outlook Why  the  SM Why  the  MSSM ObservaNon: Given  the  soluNon                                                                                                    for  the  algebra  we  we  can  take  not   only                                                                                                      but  in  addiNon  to  that  also  the  soluNon                                                                                            for  each  of  the  two  components  of  the  algebra: with SM  parNcles “Gaugino’s” There  is  an  R-­‐parity  operator: (From                                                                                                                                                    ) (Krajewski  diagrams:                                    representaNons  have  a  solid  fill.)   Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  58. 58. The  project Approach ApplicaIon Preliminary  results Outlook The  supersymmetric  spectral  triple  for  the  MSSM’ Three  steps  to  the  (MS)SM IniNal  situaNon: 1. Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  59. 59. The  project Approach ApplicaIon Preliminary  results Outlook The  supersymmetric  spectral  triple  for  the  MSSM’ Three  steps  to  the  (MS)SM IniNal  situaNon: 1. Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  60. 60. The  project Approach ApplicaIon Preliminary  results Outlook The  supersymmetric  spectral  triple  for  the  MSSM’ Three  steps  to  the  (MS)SM IniNal  situaNon: 1. Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  61. 61. The  project Approach ApplicaIon Preliminary  results Outlook The  supersymmetric  spectral  triple  for  the  MSSM’ Three  steps  to  the  (MS)SM: A vs A^C 1. 2. As  the  result  of  a  grading: Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  62. 62. The  project Approach ApplicaIon Preliminary  results Outlook The  supersymmetric  spectral  triple  for  the  MSSM’ Three  steps  to  the  (MS)SM: A vs A^C 1. 2. As  the  result  of  a  grading: Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  63. 63. The  project Approach ApplicaIon Preliminary  results Outlook The  supersymmetric  spectral  triple  for  the  MSSM’ Three  steps  to  the  (MS)SM: A vs A^C 1. 2. As  the  result  of  a  grading: Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  64. 64. The  project Approach ApplicaIon Preliminary  results Outlook The  supersymmetric  spectral  triple  for  the  MSSM’ Three  steps  to  the  (MS)SM: A vs A^C 1. 2. As  the  result  of  a  grading: Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  65. 65. The  project Approach ApplicaIon Preliminary  results Outlook The  supersymmetric  spectral  triple  for  the  MSSM’ Three  steps  to  the  (MS)SM: A vs A^C 1. 2. As  the  result  of  a  grading: Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  66. 66. The  project Approach ApplicaIon Preliminary  results Outlook The  supersymmetric  spectral  triple  for  the  MSSM’ Three  steps  to  the  (MS)SM: A vs A^C 1. 2. As  the  result  of  a  grading: Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  67. 67. The  project Approach ApplicaIon Preliminary  results Outlook The  supersymmetric  spectral  triple  for  the  MSSM’ Three  steps  to  the  (MS)SM: 1. 2. 3. By  adding  a  Majorana  mass for  the  right  handed  neutrino   Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  68. 68. The  project Approach ApplicaIon Preliminary  results Outlook The  supersymmetric  spectral  triple  for  the  MSSM’ Three  steps  to  the  (MS)SM: 1. 2. 3. By  adding  a  Majorana  mass for  the  right  handed  neutrino   Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  69. 69. The  project Approach ApplicaIon Preliminary  results Outlook The  supersymmetric  spectral  triple  for  the  MSSM’ Three  steps  to  the  (MS)SM: 1. 2. 3. By  adding  a  Majorana  mass for  the  right  handed  neutrino   Bino Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  70. 70. The  project Approach ApplicaIon Preliminary  results Outlook The  supersymmetric  spectral  triple  for  the  MSSM’ Three  steps  to  the  (MS)SM: 1. 2. 3. By  adding  a  Majorana  mass for  the  right  handed  neutrino   Bino Gluino Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  71. 71. The  project Approach ApplicaIon Preliminary  results Outlook The  supersymmetric  spectral  triple  for  the  MSSM’ Three  steps  to  the  (MS)SM: Wino/Zino 1. 2. 3. By  adding  a  Majorana  mass for  the  right  handed  neutrino   Bino Gluino Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  72. 72. The  project Approach ApplicaIon Preliminary  results Outlook The  supersymmetric  spectral  triple  for  the  MSSM’ Three  steps  to  the  (MS)SM: Higgsinos Wino/Zino 1. 2. 3. By  adding  a  Majorana  mass for  the  right  handed  neutrino   Bino Gluino Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  73. 73. The  project Approach ApplicaIon Preliminary  results Outlook The  supersymmetric  spectral  triple  for  the  MSSM’ Three  steps  to  the  (MS)SM: Higgsinos Wino/Zino +  new  parNcles 1. 2. 3. By  adding  a  Majorana  mass for  the  right  handed  neutrino   Bino Gluino Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  74. 74. Wednesday, May 30, 2012 Prel PRELIMINARY  RESULTS
  75. 75. The  project Approach ApplicaNon Preliminary  results Outlook Gauge  group  |  UnificaNon The  gauge  group: is  sNll Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  76. 76. The  project Approach ApplicaNon Preliminary  results Outlook Gauge  group  |  UnificaNon The  gauge  group: is  sNll We  sNll  have  coupling  constant  unificaNon: Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  77. 77. The  project Approach ApplicaNon Preliminary  results Outlook Gauge  group  |  UnificaNon The  gauge  group: is  sNll We  sNll  have  coupling  constant  unificaNon: This  happens  only  because  we  have  more  parNcles  than  the  MSSM  itself   provides! Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  78. 78. The  project Approach ApplicaNon Preliminary  results Outlook Fermion  doubling  |  Chiral  anomalies Copies  of  fermions  exceed  those  of  gaugino’s  by  a  factor  of  four. Change  inner  product  in: Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  79. 79. The  project Approach ApplicaNon Preliminary  results Outlook Fermion  doubling  |  Chiral  anomalies Copies  of  fermions  exceed  those  of  gaugino’s  by  a  factor  of  four. Change  inner  product  in: Hypercharges: Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  80. 80. The  project Approach ApplicaNon Preliminary  results Outlook Fermion  doubling  |  Chiral  anomalies Copies  of  fermions  exceed  those  of  gaugino’s  by  a  factor  of  four. Change  inner  product  in: Hypercharges: All  come  in  pairs  of  opposite  charges:  chiral  anomalies  cancel Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  81. 81. The  project Approach ApplicaNon Preliminary  results Outlook Comments  on  supersymmetry   NCG  treats  bosons  &  fermions  differently No  auxiliary  fields  (on-­‐shell  descripNon) AutomaNcally  broken  by  sfermion  masses Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  82. 82. The  project Approach ApplicaNon Preliminary  results Outlook Comments  on  supersymmetry   NCG  treats  bosons  &  fermions  differently No  auxiliary  fields  (on-­‐shell  descripNon) AutomaNcally  broken  by  sfermion  masses Nonetheless:  definitely  susy-­‐like  properIes Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  83. 83. The  project Approach ApplicaNon Preliminary  results Outlook Comments  on  supersymmetry   NCG  treats  bosons  &  fermions  differently No  auxiliary  fields  (on-­‐shell  descripNon) AutomaNcally  broken  by  sfermion  masses Nonetheless:  definitely  susy-­‐like  properIes Try  to  prove  susy  modulo  sfermion  potenNal  terms: 1.  prove  susy  for  both  soluNons  given  by  C&C:     Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  84. 84. The  project Approach ApplicaNon Preliminary  results Outlook Comments  on  supersymmetry   NCG  treats  bosons  &  fermions  differently No  auxiliary  fields  (on-­‐shell  descripNon) AutomaNcally  broken  by  sfermion  masses Nonetheless:  definitely  susy-­‐like  properIes Try  to  prove  susy  modulo  sfermion  potenNal  terms: 1.  prove  susy  for  both  soluNons  given  by  C&C:     2.  prove  that  susy  stays  intact  upon  breaking Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  85. 85. Wednesday, May 30, 2012 OUT OUTLOOK
  86. 86. The  project Approach ApplicaNon Preliminary  results Outlook Summary  &  Outlook ✓ ‘Supersymmetric  spectral  triple’ ? Supersymmetric  acNon  /  explicit  susy  transformaNons Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  87. 87. The  project Approach ApplicaNon Preliminary  results Outlook Summary  &  Outlook ✓ ‘Supersymmetric  spectral  triple’ ? Supersymmetric  acNon  /  explicit  susy  transformaNons ✓ Applied  to  SM-­‐algebra  gives  MSSM’ ✓ Gauge  group  intact,  anomaly  free  theory ✓ Coupling  constant  unificaNon   ? Role  &  effects  extra  parNcles? Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  88. 88. The  project Approach ApplicaNon Preliminary  results Outlook Summary  &  Outlook ✓ ‘Supersymmetric  spectral  triple’ ? Supersymmetric  acNon  /  explicit  susy  transformaNons ✓ Applied  to  SM-­‐algebra  gives  MSSM’ ✓ Gauge  group  intact,  anomaly  free  theory ✓ Coupling  constant  unificaNon   ? Role  &  effects  extra  parNcles? ? PredicNons? Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
  89. 89. The  project Approach ApplicaNon Preliminary  results Outlook Summary  &  Outlook ✓ ‘Supersymmetric  spectral  triple’ ? Supersymmetric  acNon  /  explicit  susy  transformaNons ✓ Applied  to  SM-­‐algebra  gives  MSSM’ ✓ Gauge  group  intact,  anomaly  free  theory ✓ Coupling  constant  unificaNon   ? Role  &  effects  extra  parNcles? ? PredicNons? For  more  (conclusive)  results:  stay  tuned! Thijs  van  den  Broek  (RU  Nijmegen) NoncommutaNve  geometry  &  supersymmetryWednesday, May 30, 2012
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