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Aninda Sinha IISc, Bangalore, India & Perimeter Institute, Canada. Sixth International Conference on Physics and Astrophysics of Quark Gluon Plasma. Goa, India. 6-10 December 2010. Aninda Sinha, IISc 1 Quick review of AdS/CFT Progress on viscosity bound Cavitation and breakdown of hydrodynamics RG flows, nature of quantum liquids Conclusions Aninda Sinha, IISc 2 Quick review of AdS/CFT Progress on viscosity bound Cavitation and breakdown of hydrodynamics RG flows, nature of quantum liquids Conclusions Aninda Sinha, IISc 3 What does superstring theory have to say about the quark-gluon plasma? String theory has recently provided new analytic tools to study certain nonAbelian gauge theories (similar to QCD) – suited for strong coupling and dynamical questions AdS/CFT correspondence (Anti-de Sitter/Conformal Field Theory Correspondence) (Maldacena; Witten; Gubser, Klebanov & Polyakov, . . . ) Aninda Sinha, IISc 4 (Maldacena; Witten; Gubser, Klebanov & Polyakov, . . . ) AdS/CFT correspondence: closed strings on AdS5 X S5 with RR flux Nc (3+1)-dimensional N=4 SU(Nc) super-Yang-Mills anti-de Sitter (AdS) space: homogeneous and isotropic geometry with constant negative curvature Aninda Sinha, IISc 5 AdS/CFT correspondence: conformal field theory anti-de Sitter space quantum gravity • negative cosmological constant • d+1 spacetime dimensions quantum field theory • no scale (at quantum level) • d spacetime dimensions “holography” • no gravity Favorite example: Type IIb superstrings on AdS5 X S5 with RR flux Nc (3+1)-dimensional N=4 SU(Nc) super-Yang-Mills Aninda Sinha, IISc 6 AdS/CFT correspondence: conformal field theor anti-de Sitter space quantum gravity • negative cosmological constant • d+1 spacetime dimensions quantum field theory • no scale (at quantum level) • d spacetime dimensions “holography” • no gravity classical gravity with small curvatures large central charge ( ) strong coupling ( ) Aninda Sinha, IISc 7 anti-de Sitter space: maximally symmetric geometry with negative curvature Boundary (d dimensions) (simplest) solution of Einstein’s equations with negative Λ: Bulk (d+1 dimensions) Aninda Sinha, IISc 8 anti-de Sitter space: maximally symmetric geometry with negative curvature Boundary (d dimensions) Bulk (d+1 dimensions) “redshift”: proper distances get smaller for small r 9 boundary/CFT metric Aninda Sinha, IISc anti-de Sitter space: maximally symmetric geometry with negative curvature Boundary (d dimensions) UV IR Horizon AdS Black Hole = CFT Thermal State Aninda Sinha, IISc 10 QCD T=0 N=4 SYM Nc=3=Nf , confinement, discrete spectrum, scattering, . . . . Nc large, Nf/Nc small, deconfined, conformal, supersymmetric, . . . . Universal behaviour?? very different !! strongly-coupled plasma of gluons & fundamental matter T>TC deconfined, screening, finite corr. lengths, . . . strongly-coupled plasma of gluons & adjoint (and fundamental) matter deconfined, screening, finite corr. lengths, . . . very similar !! remains strongly-coupled T>>TCruns to weak coupling very different !! Aninda Sinha, IISc 11 Quick review of AdS/CFT Progress on viscosity bound Cavitation and breakdown of hydrodynamics RG flows, nature of quantum liquids Conclusions Aninda Sinha, IISc 12 What about shear viscosity? • AdS/CFT duality relates hydrodynamic properties of strongly-coupled plasma to dynamics of AdS black hole deviations from equilibrium in plasma gravitational probes/fluctuations • variety of transport coefficients: shear viscosity, bulk viscosity, charge diffusion, . . . . Shear viscosity: defined by Kubo formula • AdS/CFT evaluates as correlator of gravitons: [Policastro, Son & Starinets; Son & Starinets; Herzog & Son] Aninda Sinha, IISc 13 Shear viscosity: “gravity waves in the fifth dimension” AdS5 boundary dissipation from absorption by BH horizon Black hole horizon horizo • gravity result: • horizon entropy: • universal result for all known theories with Einstein gravity dual: in units of [Kovtun, Son & Starinets; Buchel & Liu; Benincasa, Buchel &Naryshkin; Iqbal Aninda Sinha, IISc & Liu; . . . ] 14 is really small! • KSS conjecture: Aninda Sinha, IISc (hep-th/0405231) 15 It is now known that several CFTs with fundamental matter and holographic duals violate the bound [Kats, Petrov; Brigante et al; Buchel, Myers, AS]. The real question is: Is there a bound at all? Search using holographic methods how low you can drive the bound. Aninda Sinha, IISc 16 AdS/sQGP phenomenology: Can we make precise comparisons?[Buchel, Myers, AS] • imagine quark-gluon plasma is described by an effective CFT • AdS/CFT allows us to study 4D CFT’s with 5D gravity action: • various interactions characterize the conformal algebra (i.e., n-point functions for Tab) • adding more higher curvature corrections expands universality class by adding additional CFT parameters (1/Nc and 1/λ corrections) • can we model sQGP results with CFT and dual gravity theory?? • does QCD plasma fit into some “holographic” universality class?? Aninda Sinha, IISc 17 AdS/sQGP phenomenology: • assume effective CFT describes sQGP with few parm’s: a, c, • match physics with dual gravity theory with few coefficients: • constraining framework needs many handles on sQGP Einstein gravity • is dual of sQGP close to Einstein gravity? • seems need not be close to Einstein gravity? sQGP ?? • consistency of dual gravity constrains parameters! Aninda Sinha, IISc 18 Shear viscosity of N=4 super Yang Mills at finite temperature strong couling using AdS/CFT [Buchel, Liu, Starinets, 2004, Myers, Paulos, AS, 2008] TRUE FOR ALL THEORIES WITH UNIVERSAL !! GRAVITY DUALS >0, is this true always? ANS: NO. [Kats, Petrov;Buchel, Myers, AS 2008] Aninda Sinha, IISc 19 Superconformal gauge theories with marginal gauge coupling: • for example: sCFT’s with SU(Nc) gauge group matter fields N=4 SYM • shear viscosity: [Buchel, Myers ,AS] These violate KSS bound!! Prediction fortheories lattice? Adding fundamental Aninda Sinha, IISc matter will lower the ratio at strong coupling. 20 What is the minimum in a consistent higher derivative theory? To answer this question we need 1. A model with EXACT black hole solutions—highly nontrivial as equations are generally very complicated. 2. Constraints on the parameter space—use positive energy correlations, microcausality. 3. A brave heart! Aninda Sinha, IISc 21 Aninda Sinha, IISc 22 Pseudo-topological theory causality constraints [Myers, Paulos, AS] Plot h/s for Gauss-Bonnet in arbitrary dimensions [Buchel, Escobedo, Myers, Paulos, Smolkin, AS] Minimum value Having a maximum means in these theories the ratio cannot be too large! Aninda Sinha, IISc 23 Noronha, Gyulassy and Torrieri apply AdS/CFT phenomenology proposed in Buchel, Myers, AS. They find elliptic flow of bulk hadrons and heavy quark jet quenching can be simultaneously accounted by choosing ‘t Hooft coupling . Weakly coupled QGP models have not been able to explain this data. Will be very interesting to enlarge ensemble of observables to see how far this program can be pushed. Aninda Sinha, IISc 24 Quick review of AdS/CFT Progress on viscosity bound Cavitation and breakdown of hydrodynamics RG flows, nature of quantum liquids Conclusions Aninda Sinha, IISc 25 Rajagopal and Tripuraneni ask: Do the hydro equations know their own doom? Very interesting to explore this question. For simplicity consider boost invariant flow. Aninda Sinha, IISc 26 CAVITATION 0908.1785 [hep-ph] Aninda Sinha, IISc 27 Some parameters are from N=4 SYM while some are phenomenological Guesses on bulk viscosity and relaxation time Better to have single model in AdS/CFT which gives us all the parameters Aninda Sinha, IISc 28 Pheno Aninda Sinha, IISc 29 No cavitation in N=2* within Tc. Agrees with Song and Heinz 0909.1549. Aninda Sinha, IISc 30 Quick review of AdS/CFT Progress on viscosity bound Cavitation and breakdown of hydrodynamics RG flows, nature of quantum liquids Conclusions Aninda Sinha, IISc 31 Question: What is the nature of matter that is responsible for low viscosity/entropy? Interesting answer: Nickel & Son– The long distance behaviour of holographic liquids can be described by a set of emergent Goldstone bosons, interacting with a strongly coupled infrared sector. Can we usefully describe emergent phenomena in an RG context? Polchinski et al, Faulkner et al. Aninda Sinha, IISc 32 Can this be the end of story? Probably not. Observations: Bhattacharya and Minwalla have shown that thermalization differs in odd and even dimensions. What is different in odd and even dimensions? Answer: Trace anomalies. Mottola et al (1006.3567) claim that there is a new collective mode (scalar) that emerges in the IR coupled to gravity in even dimesions. Quite plausible that this is responsible for the different thermalization. Can we do a calculation to test this hypothesis? Aninda Sinha, IISc 33 AdS/CFT has been a very useful tool to probe strong coupling regime of interesting field theories. It has at least sparked the imagination of many. Still a long way to go before we can make contact with reality. More conceptual and (more importantly) technical tools are necessary. LOTS TO DO!! Aninda Sinha, IISc 34 Rob Myers, Miguel Paulos, Alex Buchel, Louis Leblond, Ola Klimek for collaborations. Bikash Sinha for encouraging me to think about the nature of quantum liquids. The organizers for a great conference. Aninda Sinha, IISc 35