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13.30 o1 m visser

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Research 1: M Visser

Research 1: M Visser

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  • 1. VUW Victoria University of Wellington ¯ Te Whare W¯nanga o te Upoko o te Ika a Maui a Hoˇava gravity r Matt Visser NZIP 2011 Wellington Monday 17 October 2011Matt Visser (VUW) Hoˇava gravity r NZIP 2011 1 / 34
  • 2. Abstract: VUW Hoˇava gravity is a recent (Jan 2009) idea in theoretical physics for r trying to develop a quantum field theory of gravity, an idea that has already generated approximately 575 scientific articles. It is not a string theory, nor loop quantum gravity, but is instead a quantum field theory that breaks Lorentz invariance at ultra-high (trans-Planckian) energies, while retaining Lorentz invariance at low VUW and medium energies. Matt Visser (VUW) Hoˇava gravity r NZIP 2011 2 / 34
  • 3. Abstract: VUW The challenge is to keep the Lorentz symmetry breaking controlled and small — small enough to be compatible with experiment. I will give a very general overview of what is going on in this field, paying particular attention to the disturbing role of the scalar VUW graviton. Matt Visser (VUW) Hoˇava gravity r NZIP 2011 3 / 34
  • 4. Key questions: VUW Is Lorentz symmetry truly fundamental? Or is it just an “accidental” low-momentum emergent symmetry? Opinions on this issue have undergone a radical mutation over the last few years. Historically, Lorentz symmetry was considered absolutely fundamental — not to be trifled with — but for a number of independent reasons VUW the modern viewpoint is more nuanced. Matt Visser (VUW) Hoˇava gravity r NZIP 2011 4 / 34
  • 5. Key questions: VUW What are the benefits of Lorentz symmetry breaking? What can we do with it? Why should we care? VUW Where are the bodies buried? Matt Visser (VUW) Hoˇava gravity r NZIP 2011 5 / 34
  • 6. Hoˇava gravity: r Quantum Gravity at a Lifshitz Point. Petr Hoˇava. Jan 2009. r Physical Review D79 (2009) 084008. arXiv: 0901.3775 [hep-th] (cited 552 times; 355 published; as of 13 Oct 2011). Membranes at Quantum Criticality. Petr Hoˇava. Dec 2008. r JHEP 0903 (2009) 020. arXiv: 0812.4287 [hep-th] (cited 290 times; 199 published; as of 13 Oct 2011). Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point. Petr Hoˇava. Feb 2009. r Physical Review Letters 102 (2009) 161301. arXiv: 0902.3657 [hep-th] (cited 229 times; 155 published; as of 13 Oct 2011). Matt Visser (VUW) Hoˇava gravity r NZIP 2011 6 / 34
  • 7. Hoˇava gravity: r VUWAs of 13 Oct 2011 the Inspire bibliographic reports that(apart from Hoˇava’s own articles) this topic has generated: r 38 published papers with 100 or more citations. 41 published papers with 50–99 citations. 65 published papers with 25–49 citations. 80 published papers with 10–24 citations. VUWHowever you look at it, this topic is “highly active”. Matt Visser (VUW) Hoˇava gravity r NZIP 2011 7 / 34
  • 8. Hoˇava gravity: r VUWWarning: There has been somewhat of a tendency to charge full steam ahead with applications, (sometimes somewhat fanciful), without first fully understanding the foundations of the model. For that matter, there is still, after 2 1 years, considerable 2 disagreement as to what precise version of the model is “best”. When reading the literature, a certain amount of caution is VUW advisable... Matt Visser (VUW) Hoˇava gravity r NZIP 2011 8 / 34
  • 9. Hoˇava gravity: rMy interpretation of the central idea: Abandon ultra-high-energy Lorentz invariance as fundamental. One need “merely” attempt to recover an approximate low-energy Lorentz invariance. Typical dispersion relation: k4 ω= m2 + k 2 + + ... K2 Nicely compatible with the “analogue spacetime” programme... Matt Visser (VUW) Hoˇava gravity r NZIP 2011 9 / 34
  • 10. Quantum Field Theory — QFT: Every QFT regulator known to mankind either breaks Lorentz invariance explicitly (e.g. lattice), or does something worse, something outright unphysical. For example: Pauli–Villars violates unitarity; Lorentz-invariant higher-derivatives violate unitarity; dimensional regularization is at best a purely formal trick with no direct physical interpretation... (and which requires a Zen approach to gamma matrix algebra). Matt Visser (VUW) Hoˇava gravity r NZIP 2011 10 / 34
  • 11. QFT:Old viewpoint: If the main goal is efficient computation in a corner of parameter space that we experimentally know to be Lorentz invariant to a high level of precision, then by all means, go ahead and develop a Lorentz-invariant perturbation theory with an unphysical regulator — hopefully the unphysical aspects of the computation can first be isolated in a controlled manner, and then ultimately be banished by renormalization. This is exactly what is done, (very efficiently and very effectively), in the “standard model of particle physics”. Matt Visser (VUW) Hoˇava gravity r NZIP 2011 11 / 34
  • 12. QFT:New viewpoint: If however one has reason to suspect that Lorentz invariance might ultimately break down at ultra-high (trans–Planckian?) energies, then a different strategy suggests itself. Maybe one could use the Lorentz symmetry breaking as part of the QFT regularization procedure? Could we at least keep intermediate parts of the QFT calculation “physical”? Note that “physical” does not necessarily mean “realistic”, it just means we are not violating fundamental tenets of quantum physics at intermediate stages of the calculation. Matt Visser (VUW) Hoˇava gravity r NZIP 2011 12 / 34
  • 13. QFT:Physical but Lorentz-violating regulator: Specific dispersion relation: k4 k6 ω 2 = m2 + k 2 + 2 + 4. K4 K6 QFT propagator [momentum-space Green function]: 1 G (ω, k) = . k4 k6 ω2 − m2 + k2 + 2 K4 + 4 K6 Note rapid fall-off as spatial momentum k → ∞. This improves the behaviour of the integrals encountered in Feynman diagram calculations (QFT perturbation theory). Matt Visser (VUW) Hoˇava gravity r NZIP 2011 13 / 34
  • 14. QFT:Key result: In any (3+1) dimensional scalar QFT, with arbitrary polynomial self-interaction, this is enough (after normal ordering), to keep all Feynman diagrams finite.For details see: Lorentz symmetry breaking as a quantum field theory regulator. Matt Visser. Feb 2009. Physical Review D80 (2009) 025011. arXiv: 0902.0590 [hep-th] Related articles by Anselmi and collaborators. Matt Visser (VUW) Hoˇava gravity r NZIP 2011 14 / 34
  • 15. QFT:Key results: Gravity is a little trickier, but you can at least argue for power-counting renormalizability of the resulting QFT. This is unexpected, seriously unexpected... And yes there are still significant technical difficulties... (of which more anon)...For details see: Hoˇava’s papers. r Power-counting renormalizability of generalized Horava gravity. Matt Visser. Dec 2009. e-Print: arXiv:0912.4757 [hep-th] Matt Visser (VUW) Hoˇava gravity r NZIP 2011 15 / 34
  • 16. Implications for quantum gravity:Develop a non-standard extension of the usual ADM decomposition: Choose a “preferred foliation” of spacetime into space+time. Implicit return of the aether... Decompose the Lagrangian L = (kinetic term) − (potential term) Now add extra “kinetic” and “potential” terms, beyond the usual textbook Einstein–Hilbert Lagrangian. Matt Visser (VUW) Hoˇava gravity r NZIP 2011 16 / 34
  • 17. Hoˇava gravity: r It is roughly at this stage that Hoˇava makes his two great r simplifications: “projectability”; “detailed balance”. Even after 2 1 years — it is still somewhat unclear whether these are 2 just “simplifying ansatze” or whether they are fundamental to Hoˇava’s model. r In particular, Silke Weinfurtner, Thomas Sotiriou, and I have argued that “detailed balance” is not fundamental, and we have been carefully thinking about the issue of “projectability”. Matt Visser (VUW) Hoˇava gravity r NZIP 2011 17 / 34
  • 18. Hoˇava gravity: rEliminating detailed balance: Phenomenologically viable Lorentz-violating quantum gravity. Thomas Sotiriou, Matt Visser, Silke Weinfurtner. Apr 2009. Physical Review Letters 102 (2009) 251601. arXiv: 0904.4464 [hep-th] Quantum gravity without Lorentz invariance. Thomas Sotiriou, Matt Visser, Silke Weinfurtner. May 2009. JHEP 0910 (2009) 033. arXiv: 0905.2798 [hep-th] Matt Visser (VUW) Hoˇava gravity r NZIP 2011 18 / 34
  • 19. Projectability:What is Hoˇava’s projectability condition? rThis is the assertion that the so-called lapse function is always trivial,(or more precisely trivializable). In standard general relativity the “projectability condition” can always be enforced locally as a gauge choice; Furthermore for “physically interesting” solutions of general relativity it seems that this can always be done (more or less) globally.For this purely pragmatic reason we decided to put “projectability” off toone side for a while, and first deal with “detailed balance”. Matt Visser (VUW) Hoˇava gravity r NZIP 2011 19 / 34
  • 20. Detailed balance:What is Hoˇava’s detailed balance condition? rIt is a way of constraining the potential: V(g ) is a perfect square.That is, there is a “pre-potential” W (g ) such that: δW kl δW V(g ) = g ij g . δgjk δgliThis simplifies some steps of Hoˇava’s algebra, it makes other features rmuch worse. Matt Visser (VUW) Hoˇava gravity r NZIP 2011 20 / 34
  • 21. Detailed balance: VUWIn particular, if you assume Hoˇava’s detailed balance condition, and try to rrecover usual Einstein-Hilbert physics in the low energy regime, then: You are forced to accept a non-zero cosmological constant of the “wrong sign”. You are forced to accept intrinsic parity violation in the purely gravitational sector.The second point I could live with, the first point will require somemutilation of detailed balance. VUWSo we might as well go the whole way and discard detailed balance entirely. Matt Visser (VUW) Hoˇava gravity r NZIP 2011 21 / 34
  • 22. Discarding detailed balance:The standard Einstein–Hilbert piece of the action is now: √ SEH = ζ 2 (K ij Kij − K 2 ) + R − g0 ζ 2 g N d3 x dt.The “extra” Lorentz-violating terms are: SLV = ζ 2 ξ K 2 − g2 ζ −2 R 2 − g3 ζ −2 Rij R ij −g4 ζ −4 R 3 − g5 ζ −4 R(Rij R ij ) −g6 ζ −4 R i j R j k R k i − g7 ζ −4 R 2 R √ −g8 ζ −4 i Rjk i R jk g N d3 x dt.(Some 10 pages of careful calculation required.) Matt Visser (VUW) Hoˇava gravity r NZIP 2011 22 / 34
  • 23. Physical units: From the normalization of the Einstein–Hilbert term: g0 ζ 2 (16πGNewton )−1 = ζ 2 ; Λ= ; 2 so that ζ is identified as the Planck scale. The cosmological constant is determined by the free parameter g0 , and observationally g0 ∼ 10−123 . (Renormalized after including vacuum energy contributions.) In particular, we are free to choose the Newton constant and cosmological constant independently. (And so can be made compatible with observation.) Matt Visser (VUW) Hoˇava gravity r NZIP 2011 23 / 34
  • 24. Physical units: The Lorentz violating term in the kinetic energy leads to an extra scalar mode for the graviton, with fractional O(ξ) effects at all momenta. Phenomenologically, this behaviour is potentially dangerous and should be carefully investigated. The various Lorentz-violating terms in the potential become comparable to the spatial curvature term in the Einstein–Hilbert action for physical momenta of order ζ ζ ζ{2,3} = ; ζ{4,5,6,7,8} = . |g{2,3} | 4 |g{4,5,6,7,8} | Matt Visser (VUW) Hoˇava gravity r NZIP 2011 24 / 34
  • 25. Physical units: The Planck scale ζ is divorced from the various Lorentz-breaking scales ζ{2,3,4,5,6,7,8} . We can drive the Lorentz breaking scale arbitrarily high by suitable adjustment of the dimensionless couplings g{2,3} and g{4,5,6,7,8} . Based on his intuition coming from “analogue spacetimes”, Grisha Volovik has been asserting for many years that the Lorentz-breaking scale should be much higher than the Planck scale. This model naturally implements that idea. Matt Visser (VUW) Hoˇava gravity r NZIP 2011 25 / 34
  • 26. Hoˇava gravity — Problems and pitfalls: rWhere are the bodies buried? Projectability: This yields a spatially integrated Hamiltonian constraint rather than a super-Hamiltonian constraint. Prior structure: Is the preferred foliation “prior structure”? Or is it dynamical? Scalar graviton: As long as ξ = 0 there is a spin-0 scalar graviton, in addition to the spin-2 tensor graviton. Hierarchy problem? (Renormalizability may still require fine tuning.) Beta functions? Beyond power-counting? RG flow? (Very limited explicit calculations so far.)There is still the potential for violent conflicts with empirical reality. Matt Visser (VUW) Hoˇava gravity r NZIP 2011 26 / 34
  • 27. Graviton propagator linearized around flat space:The spin-0 scalar graviton is potentially dangerous: Binary pulsar? (Extra energy loss mechanism?) PPN physics? (Detailed solar system tests?) E¨tv¨s experiments? o o (Universality of free-fall?) Negative kinetic energy? (Between the UV conformal and IR general relativistic limits.)Lots of careful thought still needed... Matt Visser (VUW) Hoˇava gravity r NZIP 2011 27 / 34
  • 28. Spin-zero graviton:The “Healthy Extension” of Horava-Lifshitz gravity. Consistent Extension of Horava Gravity. Diego Blas, Oriol Pujolas, Ssergey Sibiryakov. Sep 2009. Physical Review Letters 104 (2010) 181302. e-Print: arXiv:0909.3525 [hep-th] Models of non-relativistic quantum gravity: the good, the bad and the healthy. Diego Blas, Oriol Pujolas, Sergey Sibiryakov. Jul 2010. JHEP 1104 (2011) 018 e-Print: arXiv:1007.3503 [hep-th]Key idea: Make the “preferred foliation” dynamical.(Stably causal spacetime with preferred “cosmic time”.) Matt Visser (VUW) Hoˇava gravity r NZIP 2011 28 / 34
  • 29. Spin-zero graviton:Search for “analogue spacetime” hints: Emergent gravity at a Lifshitz point from a Bose liquid on the lattice. Cenke Xu, Petr Hoˇava. Mar 2010. r Physical Review D81 (2010) 104033. e-Print: arXiv:1003.0009 [hep-th]Add an extra gauge symmetry: General covariance in quantum gravity at a Lifshitz point. Petr Horava, Charles M. Melby-Thompson. Jul 2010. Physical Review D82 (2010) 064027. e-Print: arXiv:1007.2410 [hep-th]Extra symmetry not related to diffeomorphism invariance. Matt Visser (VUW) Hoˇava gravity r NZIP 2011 29 / 34
  • 30. Spin-zero graviton:Projectability? Projectable Horava-Lifshitz gravity in a nutshell. Silke Weinfurtner, Thomas P. Sotiriou, Matt Visser. Feb 2010. Journal of Physics Conference Series 222 (2010) 012054. e-Print: arXiv:1002.0308 [gr-qc]Other? Status of Horava gravity: A personal perspective. Matt Visser. Mar 2011. Journal of Physics Conference Series 314 (2011) 012002. e-Print: arXiv:1103.5587 [hep-th] Matt Visser (VUW) Hoˇava gravity r NZIP 2011 30 / 34
  • 31. Spin-zero graviton: VUWTo get rid of the scalar graviton, the choices seem to be: Approximately decouple the scalar mode? Kill the scalar mode with more symmetry? Kill the scalar mode with more a priori restrictions on the metric? (Even more restrictions than projectability?)While significant progress is being made, VUWnone of these approaches is as yet fully satisfying. Matt Visser (VUW) Hoˇava gravity r NZIP 2011 31 / 34
  • 32. Causal Dynamical Triangulation — CDT:Comparing CDT with Hoˇava gravity: r Hoˇava’s spectral dimension paper. r CDT meets Horava-Lifshitz gravity. J. Ambjorn, A. Gorlich, S. Jordan, J. Jurkiewicz, R. Loll. Feb 2010. Physics Letters B690 (2010) 413–419. e-Print: arXiv:1002.3298 [hep-th] Spectral dimension as a probe of the ultraviolet continuum regime of causal dynamical triangulations. Thomas P. Sotiriou, Matt Visser, Silke Weinfurtner. May 2011. Physical Review Letters 107 (2011) 131303. e-Print: arXiv:1105.5646 [gr-qc] Matt Visser (VUW) Hoˇava gravity r NZIP 2011 32 / 34
  • 33. s for CDT in this regime. enough, curvature effects his procedure will not uniquely determine all — the Causal Dynamical Triangulation of CDT:effects become subdominaameters of HL gravity. First of all, it is already clear regime where both effects c 1 (color online).CDT The spectral dimension as a function of (fictitious) diffusion time s (semi Comparing (a) numerical experiments with predictions from ats for CDT for simulation withrelation simplices, whereas the red solid line represent the fit Hoˇava-type dispersion 200 000 in 2+1 dimensions. 3-parameter fit. rre discretium effects are important is lightly shaded. The region where curvature effects d mediate Mattthe ultraviolet continuum region. (b) Zoom into the latter region. 2011 Individual is Visser (VUW) Hoˇava gravity r NZIP (c) 33 / 34
  • 34. Summary: —— VUW —— Still a very active field... Initial feeding frenzy somewhat subsided... Very real physics challenges remain... —— VUW —— Matt Visser (VUW) Hoˇava gravity r NZIP 2011 34 / 34