Transcript AdS/CFT and sQGP

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
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Quick review of AdS/CFT
Progress on viscosity bound
Cavitation and breakdown of hydrodynamics
RG flows, nature of quantum liquids
Conclusions
Aninda Sinha, IISc
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Quick review of AdS/CFT
Progress on viscosity bound
Cavitation and breakdown of hydrodynamics
RG flows, nature of quantum liquids
Conclusions
Aninda Sinha, IISc
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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, . . . )
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(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
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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
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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 (
)
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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)
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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
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boundary/CFT metric
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anti-de Sitter space:
maximally symmetric geometry with negative curvature
Boundary
(d dimensions)
UV
IR
Horizon
AdS Black Hole = CFT Thermal State
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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 !!
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Quick review of AdS/CFT
Progress on viscosity bound
Cavitation and breakdown of hydrodynamics
RG flows, nature of quantum liquids
Conclusions
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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]
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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
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& Liu; . . . ]
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is really small!
•
KSS conjecture:
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(hep-th/0405231)
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It is now known that several CFTs with
fundamental matter and holographic duals
violate the bound [Kats, Petrov; Brigante et al; Buchel,
Myers, AS].
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The real question is: Is there a bound at all?
Search using holographic methods how low
you can drive the bound.
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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??
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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!
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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]
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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
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IISc
matter will lower the ratio at strong
coupling.
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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!
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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!
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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.
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Quick review of AdS/CFT
Progress on viscosity bound
Cavitation and breakdown of hydrodynamics
RG flows, nature of quantum liquids
Conclusions
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Rajagopal and Tripuraneni ask: Do the hydro
equations know their own doom?
Very interesting to explore this question. For
simplicity consider boost invariant flow.
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CAVITATION
0908.1785 [hep-ph]
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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
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Pheno
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No cavitation in
N=2* within Tc.
Agrees with Song and
Heinz 0909.1549.
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
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Quick review of AdS/CFT
Progress on viscosity bound
Cavitation and breakdown of hydrodynamics
RG flows, nature of quantum liquids
Conclusions
Aninda Sinha, IISc
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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.
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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?
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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!!
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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.
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