The First Order Stark Effect In Hydrogen For $n=3$
YRM 2016 - JM ASHFAQUE
1. F-Theory GUTs & The LHC Diphoton Excess
JOHAR M. ASHFAQUE
University of Liverpool
Based on arXiv:1607.03076
JOHAR M. ASHFAQUE YRM 2016
2. The Standard Model of Particle Physics:
SUp3q¢SUp2q¢Up1q
JOHAR M. ASHFAQUE YRM 2016
3. Then Why String Theory?
To incorporate GRAVITY with the Standard Model gauge
group SUp3q¢SUp2q¢Up1ql jh n
SUp5q
l jh n
SOp10q
l jh n
E6ÑSOp10q¢Up1q
.
JOHAR M. ASHFAQUE YRM 2016
4. Why (Bosonic) String Theory Is Not The Complete Story?
JOHAR M. ASHFAQUE YRM 2016
5. Why (Bosonic) String Theory Is Not The Complete Story?
The ground state of the spectrum always contains a tachyon.
As a consequence, the vacuum is unstable.
JOHAR M. ASHFAQUE YRM 2016
6. Why (Bosonic) String Theory Is Not The Complete Story?
The ground state of the spectrum always contains a tachyon.
As a consequence, the vacuum is unstable.
Does not contain fermions. Where is the matter?
JOHAR M. ASHFAQUE YRM 2016
8. Heterotic Superstrings
There are two heterotic string theories, one associated to the
gauge group
E8
ljhn
observable
¢ E81
ljhn
hidden
and the other to
SOp32q
or more precisely
Spinp32q{Z2
which is the double cover of SOp32q.
JOHAR M. ASHFAQUE YRM 2016
9. The Importance of Geometry In Physics
Useful insight
Model Building
Low Energy Effective Models of String theory
Desire models with
4 flat space-time dimensions
3 generations of matter
N 1 SUSY
JOHAR M. ASHFAQUE YRM 2016
10. How F-Theory Saves The Day?
How can we hope to say anything about particle physics given
the complexity of string vacua?
Apparent unification of couplings in MSSM at
MGUT 1016 GeV
Ñ MSUSY 3 MGUT 3 MPlanck
JOHAR M. ASHFAQUE YRM 2016
11. The Idea
If we were to compactify type II-B theory on some manifold B then
this could be expressed in terms of F-theory compactified on a
larger manifold A with specific properties that A has the structure
of a fibre bundle and is an elliptic fibration of the manifold B.
π : CYn 1 Ñ Bn
JOHAR M. ASHFAQUE YRM 2016
12. Model Building Elements
Each lower-dimensional subspace provides an important model
building element
Dimension Ingredient Complex Enhancements
Codimension
10D Gravity - -
8D Gauge Theory 1 -
6D Matter 2 Rank 1
4D Yukawa Couplings 3 Rank 2
JOHAR M. ASHFAQUE YRM 2016
13. The SUp5q GUT: Pictorially
The six extra dimensions are compactified on B3 whereas the
SUp5q degrees of freedom are localized on the submanifold SGUT .
The gauge bosons live on the bulk of SGUT but the chiral
multiplets are localized on complex matter curves. At the
intersection of two matter curves a Yukawa coupling develops.
JOHAR M. ASHFAQUE YRM 2016
14. The SUp5q Matter Curves: Viewing The Enhancements
¥α1
¡¥α2
¡¥α3
¡¥α4
l jh n
A4
¥ ñ ¥α1
¡¥α2
¡¥α3
¡¥α4
¡¥α5
l jh n
A5
Or
¥α1
¡¥α2
¡¥α3
¡¥α4
l jh n
A4
¥ ñ ¥α1
¡¥α2
¡
¥α5
|
¥α3
¡¥α4
l jh n
D5
JOHAR M. ASHFAQUE YRM 2016
15. The SUp5q Yukawa Points: Viewing The Enhancements
¥α1
¡¥α2
¡¥α3
¡¥α4
¡¥α5
l jh n
A5
¥ ñ ¥α1
¡¥α2
¡¥α3
¡¥α4
¡¥α5
¡¥α6
l jh n
A6
Or
¥α1
¡¥α2
¡¥α3
¡¥α4
¡¥α5
l jh n
A5
¥ ñ ¥α1
¡¥α2
¡¥α3
¡
¥α6
|
¥α4
¡¥α5
l jh n
D6
Or
¥α1
¡¥α2
¡
¥α5
|
¥α3
¡¥α4
l jh n
D5
¥ ñ ¥α1
¡¥α2
¡
¥α6
|
¥α3
¡¥α4
¡¥α5
l jh n
E6
JOHAR M. ASHFAQUE YRM 2016
16. GUT Breaking Methods 1
Adjoint matter - undesirable phenomenology
No setup incorporating dynamical GUT breaking
Discrete Wilson lines on 7-brane world-volume. But discrete
symmetries have fixed points leading to singularities on
7-brane world-volume
JOHAR M. ASHFAQUE YRM 2016
17. GUT Breaking Methods 1
GUT breaking by Up1q fluxes and is something specific to
F-Theory
JOHAR M. ASHFAQUE YRM 2016
18. The SM Embedding In The 27
E6 Ñ SOp10q¢Up1qζ
Ñ rSUp5q¢Up1qζ1 s¢Up1qζ
Ñ rSUp3q¢SUp2q¢Up1qζ2 s¢Up1qζ1 ¢Up1qζ
27
6
99999998
99999997
161
2
FL FR pQ, uc, dc, L, ec, Nq
Ñ
Q uc
ec
¨
dc
L
¨
N
10¡1 D h pD, D, H, Hq
Ñ
D
H
¨
D
H
¨
12 S Ñ S
JOHAR M. ASHFAQUE YRM 2016
19. Recently At The LHC...
D D, H
S
g
g
γ
γ
Figure: (D Dq € 10 of SOp10q contribute to the diphoton signal
observed at the LHC.
JOHAR M. ASHFAQUE YRM 2016
