Insight into strong coupling

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2 Thank you 2012

3 Insight into strong coupling Many faces of holography: Top-down studies (string/m-theory based) Bottom-up approaches pheno applications to QCD-like and condensed matter systems (e.g. Umut s talk) valuable tool for probing thermal and hydrodynamic properties of strongly coupled field theories few theoretical tools available

4 Microscopic descriptions of such systems is challenging often we want their macroscopic behavior, at large distances and long time scales system typically exhibits universal features (independent of details of underlying micro description) Given exotic nature of AdS/CFT constructions, crucial to find universal properties: gain intuition about real systems in same universality class input into realistic simulations

5 Outline Focus on a particular universal property, η / s Lessons we learned from: String theory/sugra constraints Consistency of the theory as a relativistic QFT toy models not realized in string theory Emphasize: interesting behavior in systems with very different physics in IR vs UV Work with: J.Liu, K. Hanaki, P. Szepietowski (Michigan) A. Buchel (PI) arxiv: , , arxiv: arxiv:1108.xxxx arxiv: (Review)

6 Why interest in η / s?

7 I) universality of η /s For N = 4 SU(N) SYM plasma [PSS hep-th/ ] (planar limit, infinite t Hooft coupling) UNIVERSAL universal in all gauge theories with Einstein gravity duals [Buchel, Liu th/ ] regardless of matter content amount of SUSY conformality with or without chemical potential

8 II) elliptic flow measurements at RHIC RHIC DATA very small η / s for QGP comparable to 1/4π well described by hydrodynamics with a very small shear viscosity/entropy density ratio -- perfect fluid DATA FAVORS (e.g. Song et al ) Contrast to weak coupling calculations in thermal gauge theories:

9 Order of magnitude agreement with data large effort to use ads/cft to probe transport properties of sqgp

10 Can we use CFTs to probe QCD? N = 4 SYM at finite T somewhat exotic but some features qualitatively similar: For T ~ T c - 3T c Both strongly coupled QGP is nearly conformal (small bulk viscosity away from T c ) Some properties may be universal Karsch, hep-lat/ RHIC ~ 200 GeV LHC ~ 2.7 TeV generic relations provide INPUT into realistic simulations of sqgp

11 Shear Viscosity Bound agrees well with naïve dilute gas approximation suggesting QM bound: Conjecture that any fluid in nature would obey a bound: [Kovtun,Son,Starinets th ] FUNDAMENTAL IN NATURE?

12 Natural Next Step: Role of Higher Derivatives? Motivations? Ratio is universal in Einstein GR: Testing validity of bound More than that: How does it change with higher derivative corrections? role of string theory constraints on hydrodynamics (if any) Dependence of eta/s on physical parameters of the theory (various charges, chemical potential, ) CFT side: Note: leading sugra approximation hides any finite interesting sub-structure (eta/s is universal) corrections

13 String Construction Satisfying Bound Leading α correction on AdS 5 x S 5 (N = 4 SYM) increased the ratio [Buchel,Liu,Starinets th/ ] in Type IIB finite λ correction to N = 4 SYM

14 String Construction Violating Bound Kats & Petrov (arxiv: ) Type IIB on (decoupling limit of N D3 s with collection of D7 s and 07) small violation for c 3 > 0 c 3 from effective action on world-volume of D7/07 system (determined by fundamental matter content of theory)

15 SUSY completion of R 2 terms [SC,K.Hanaki,J.Liu,P.Szepietowski, , , ] So far KP only string theory example of bound violation (particular construction with fixed matter content) We wanted to explore: Role of chemical potential (R-charge) on the bound no effect at two-derivative level (universality) with higher derivatives, is bound restored with sufficiently large chemical potential? Role of SUSY/stringy constraints want consistent string theory reductions corrections constrained by supersymmetry

16 Corrections to η/s at finite chemical potential [arxiv: , SC,K.Hanaki,J.Liu,P.Szepietowski] The setup: D=5 N = 2 gauged SUGRA (electrically charged black holes) To leading order: higher derivative corrections start at R 2 (sensitive to amount of SUSY) include the mixed gauge-gravitational CS term:

17 SUSY R 2 terms in 5D Instead of brute-force compactification (on Sasaki-Einstein), make use of SUSY [Hanaki,Ohashi,Tachikawa, th/ ] SUSY completion of mixed CS term coupled to arbitrary # of vector multiplets Off-shell formulation of N=2, D=5 gauged SUGRA (superconformal formalism). End Result off shell action, lots of auxiliary fields, supersymmetric curvature-squared term in 5D

18 On-shell Lagrangian (minimal SUGRA) [arxiv: , SC,K.Hanaki,J.Liu,P.Szepietowski] controls strength of higher derivative terms c 2 can be related to the central charges of dual UV CFT via: Holographic Interpretation trace anomaly on dual gauge theory side? R-current anomaly

19 The Link to the Central Charges For us: 4D CFT with N=1 SUSY 4D CFT central charges a,c defined in terms of trace anomaly: (CFT coupled to external metric) Prescription for extracting trace anomaly for higher derivative GR: sensitive to higher derivatives For us:

20 To recap: R 2 Correction will correspond to a 1/N correction Contrast to IIB on AdS 5 x S 5 Note: these are not 1-loop corrections in the bulk (open string effects instead)

21 Back to Hydrodynamics of R-charged black-holes

22 Shear Viscosity from AdS/CFT Relativistic Hydrodynamics: η can be extracted from correlators of the boundary stress tensor (Kubo s formula) effective description of dynamics of system at large wavelengths and long time scales

23 Back to Hydrodynamics of R-charged black-holes Putting all ingredients together electrically charged black holes Suprisingly simple dependence on R-charge: some form of universality?

24 Features Bound violated for c-a > 0 (and finite N effect) R-charge makes violation worse Eta/s affected only by terms with explicit Riemann tensor: reminiscent of Wald s entropy formula SUSY completion did not play any role (although SUSY does affect form of c,a) Universality seemingly lost with higher derivatives Possible connection with weak gravity conjecture and sign of c-a [arxiv: ]

25 Violation of the bound can be traced to inequality of central charges of dual CFT: generic in superconformal gauge theories with unequal central charges [Buchel et al ]

26 In holographic models realized in string theory, violation of the KSS bound is necessarily perturbative always small (curvature corrections small)

27 Original KSS bound is clearly violated. Is there a bound at all? How low can eta/s get? Any finite (large) violation of the bound will entail working in a model of gauge/gravity duality (not a ST realization)

28 Gauss-Bonnet as a toy model [Brigante et al, , ] Black brane solutions known for finite GB coupling Finite λ GB leads to natural question: arbitrary violation of the bound? No! Must look at the consistency of the dual QFT: once the coupling becomes too large, one finds modes that propagate faster than light microcausality violation same bound by requiring positivity of energy measured by a detector in the plasma (Hofman )

29 Causality Violation and the Link to η/s In this model, consistency of the GB plasma as a relativistic QFT ensures small violation of the bound (and gives new lower bound) causality violation? bound violation this link may not be of fundamental nature [S.C.,A.Buchel arxiv: ] We considered a slight modification of the GB model, realized in a theory with a superfluid phase transition

30 Idea is generic: While transport properties are determined by the IR features of the theory, causality is determined by the propagation of UV modes (whose dynamics is not that of hydro)

31 IR vs. UV Physics shear viscosity: coupling of effective hydro description at low momentum and frequency microcausality: determined by propagation of modes in UV UV microcausality Link only if same phase of the theory extends over all energy scales (e.g. no phase transitions decoupling UV from IR) IR viscosity

32 Features of our Toy Model [S.C.,A.Buchel arxiv: ] Based on: holographic model of superfluidity proposed by GHPT (consistent truncation of Type IIB) dual operator develops a VEV below T c

33 In pictures T unbroken phase electrically charged bh Einstein GR T c broken symmetry phase bh develops scalar hair GB higher derivative corrections

34 The shear viscosity bound [arxiv: ] T expected from universality T c when λ GB is non-zero eta/s gets corrected: eta/s goes well below pure GB bound (finite λ GB ) no causality violation (down to low T, scalar when λ GB = 0 we have standard superconductor channel) (no higher derivatives) still from universality Will not set lower bound on Eta/s

35 UV/IR Decoupling UV microcausality Concrete example of decoupling of UV from IR physics Suggests that link between eta/s and causality violation is not fundamental IR viscosity Simple statement: hydrodynamics is not connected in general in a trivial way to UV CFT

36 Link to the Central Charges? Even perturbatively, here there is no link between eta/s and the UV central charges of the dual theory: η/s causality central charges of UV fixed point

37 Radial vs. Temperature Flow Well known that eta/s doesn t run in any Wilsonian sense (membrane paragigm): (trivial radial flow even with higher derivatives) In our superfluid GB model, eta/s has non-trivial behavior as a function of temperature (first explicit construction)

38 Non-trivial Eta/s flow T jump in Eta/s and temperature flow T c temperature dependence may be relevant for QGP

39 Any other ways to get interesting behavior/flow (or UV/IR decoupling ) for η/s?

40 Non-Trivial Scalar Profile? Charged dilatonic branes with Lifshitz solutions: T AdS brane Finite T solutions interpolate smoothly between the two (no phase transition) Lifshitz brane (dynam exp z)

41 Probing Lifshitz hydro with higher derivatives [SC and P. Szepietowski] T >> µ AdS brane No z-dependence (z=1) Temperature flow T << µ Lifshitz brane (dynam exp z) IR behavior (Lifshitz) is different enough from UV behavior (AdS) that we expect interesting eta/s behavior without need for phase transition

42 In Conclusion Important to ask how much mileage we can get from gravity setups to model interesting field theory systems Development of universal relations particularly valuable they provide inputs into realistic simulations of strongly coupled systems KSS bound? Clearly violated by finite N effects. New lower bound? Still unclear Transport properties: IR feature of theory micro constraints (although important for consistency of theory) should not set lower bound on eta/s

43 Although eta/s does not flow in any Wilsonian sense, it still has a different behavior in the UV than in the IR can we understand non-trivial temperature flow of eta/s in a more systematic way? possibly by extending the recent attempts to refine the Wilsonian approach to gauge/gravity duality to fully fledged viscous hydrodynamics (Bredberg,Keeler,Lysov,Strominger) (Nickel and Son) (Heemskerk and Polchinski) (Faulkner, Liu, Rangamani)

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