Download What we expect gauge/gravity duality in the near future:

What we expect gauge/gravity
duality in the near future:
from the viewpoint of hydrodynamics
and thermodynamics
CQUeST and Hanyang Univ.
Shin Nakamura
Introduction
Quark-hadron physics
RHIC, LHC experiments,
Neutron stars,
Nuclear physics
Based on QCD
Quantum Chromo-dynamics
Strong interaction at the low-energy region.
E  few times  QCD (200MeV )  1 GeV
Perturbative analysis (computations based on
Feynman diagrams) is not applicable.
Lattice QCD
A method to analyze strongly coupled systems of QCD.
QCD is defined on a discretized spacetime (lattice)
without relying on Feynman diagrams, and we can
compute everything about QCD in principle, by using
computer.
However, there are technical difficulties
in the computations of:
• time dependent systems
• systems at finite baryon chemical potential
• systems of large size
Alternative method: AdS/CFT
AdS/CFT (gauge/gravity duality)
We can analyze strongly coupled gauge theories
(of infinitely many colors) by using classical gravity
on five-dimensional curved spacetimes.
(asymptotically anti de Sitter spacetime)
A conjecture from superstring theory.
AdS/CFT: a “holography”
5d gravity
curved geometry
(negative curvature)
Alternative method: AdS/CFT
AdS/CFT (gauge/gravity duality)
We can analyze strongly coupled gauge theories
(of infinitely many colors) by using classical gravity
on five-dimensional curved spacetimes.
(asymptotically anti de Sitter spacetime)
A conjecture from superstring theory.
Why don’t we attack the problems in QCD
by using this new method?
What we have done so far
Lattice QCD has technical difficulties in
computations on:
• time dependent systems
We have attacked and keep attacking.
• systems at finite baryon chemical potential
We have attacked and keep attacking.
• systems of large size
For example, computations of inter-nucleon potentials
Time-dependent systems
Works from Hanyang University:
For example:
Shin Nakamura, Sang-Jin Sin,
JHEP 0609 (2006) 020 (hep-th/0607123)
Sang-Jin Sin, Shin Nakamura, Sang Pyo Kim
JHEP 0612 (2006) 075 (hep-th/0610113)
Keun-Young Kim, Sang-Jin Sin, Ismail Zahed,
arXiv:0707.0601
Picture of time-dependent systems
collision of heavy nuclei
5d gravity
Expanding quark-gluon plasma
at the RHIC experiment
Time-dependent curved
geometry
e.g. Kim, Sin, Zahed,
arXiv:0707.0601
The geometry is determined by 5d Einstein’s
equation and the (time-dependent) boundary
conditions.
e.g. Shin Nakamura, Sang-Jin Sin,
JHEP 0609 (2006) 020
Finite baryon chmical potential
Works from Hanyang University:
For example:
Keun-Young Kim, Sang-Jin Sin, Ismail Zahed,
hep-th/0608046
Shin Nakamura, Yunseok Seo, Sang-Jin Sin, K. P. Yogendran,
arXiv:0708.2818, arXiv:hep-th/0611021
Sang-Jin Sin,
arXiv:0707.2719
Keun-Young Kim, Sang-Jin Sin, Ismail Zahed,
arXiv:0708.1469
Shin Nakamura
arXiv:0711.1601
Picture of finite baryon density
systems
5d gravity
baryon
charge
A0: electric potential
Electric field
curved geometry
(negative curvature)
Baryon chemical potential
No such an “electric field”
in QCD.
We can investigate the phase
structure of gauge theories
T
free quarks
quark bound
states (mesons)
The details are still
under investigation.
μ
What I expect in the near future
I think there are (at least) two directions:
• Try to construct a gauge/gravity duality which is
closer to the realistic systems of QCD as much
as possible.
e.g. Sakai-Sugimoto model
talks given by Prof. Sin and Dr. Y. Kim
• Try to find a new theoretical framework by using
the simplest example of gauge/gravity dual.
(Although the gauge theory itself may not be what
we have in the nature.)
Old frameworks
“Old” frameworks for macroscopic physics:
• Finite temperature, finite density:
Thermodynamics (Boltzmann, Gibbs,….)
equilibrium, static
• If we add time-dependence further:
Hydrodynamics (Landau, ….)
local equilibrium, slightly non-static
• Static but non-equilibrium cases:
Linear response theory (Kubo, ….)
slightly non-equilibrium, static
A new framework?
Einstein may be greater than
Boltzmann, Landau, Kubo……..
• 5d gravity can describe macroscopic physics
as well as microscopic process (like scattering
amplitude of each particles).
• Emergence of the concept of temperature is
automatically encoded in the creation process
of 5d black hole.
• In principle, gauge/gravity duality does not
rely on the presence of equilibrium (or
thermodynamic limit ?).
The gauge/gravity duality may be a
good playground for inventing
a new theory of:
something going beyond thermodynamics,
hydrodynamics, or linear response theory:
• Highly non-equilibrium systems
• Highly dissipative systems
• Small volume (mesoscopic) systems
• Highly entangled systems
• ……………….
of certain (supersymmetric) gauge theories.
Anyway, it is a very interesting
subject for theoretical physicists
because,
we can play with almost all fundamental
theoretical frameworks:
Many beautiful toys
• superstring theory
are in the same box!
• general relativity
• quantum field theory
• hydrodynamics
• thermodynamics and statistical mechanics
• linear response theory
The gauge/gravity duality
• A new tool for analysis of QCD
(strongly coupled gauge theories).
We have also a chance to get a hint for:
• Highly non-equilibrium systems
• Highly dissipative systems
• Small volume (mesoscopic) systems
• Highly entangled systems