What we expect gauge/gravity duality in the near future: from the viewpoint of hydrodynamics and thermodynamics CQUeST and Hanyang Univ. Shin Nakamura

Quark-hadron physics RHIC, LHC experiments, Neutron stars, Nuclear physics Based on QCD Quantum Chromo-dynamics Strong interaction at the low-energy region. Introduction 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. A conjecture from superstring theory. (asymptotically anti de Sitter spacetime)

AdS/CFT: a “holography” 5d gravity 4d gauge theory 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. A conjecture from superstring theory. (asymptotically anti de Sitter spacetime) Why don’t we attack the problems in QCD by using this new method?

What we have done so far time dependent systems systems at finite baryon chemical potential systems of large size Lattice QCD has technical difficulties in computations on: We have attacked and keep attacking. For example, computations of inter-nucleon potentials Not yet, unfortunately, due to lack of time and man-power.

Time-dependent systems Shin Nakamura, Sang-Jin Sin, JHEP 0609 (2006) 020 (hep-th/ ) Sang-Jin Sin, Shin Nakamura, Sang Pyo Kim JHEP 0612 (2006) 075 (hep-th/ ) Keun-Young Kim, Sang-Jin Sin, Ismail Zahed, arXiv: Works from Hanyang University: For example:

Picture of time-dependent systems 5d gravity 4d gauge theory Expanding quark-gluon plasma at the RHIC experiment Time-dependent curved geometry 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 collision of heavy nuclei e.g. Kim, Sin, Zahed, arXiv:

Finite baryon chmical potential Keun-Young Kim, Sang-Jin Sin, Ismail Zahed, hep-th/ Shin Nakamura, Yunseok Seo, Sang-Jin Sin, K. P. Yogendran, arXiv: , arXiv:hep-th/ Sang-Jin Sin, arXiv: Keun-Young Kim, Sang-Jin Sin, Ismail Zahed, arXiv: Shin Nakamura arXiv: Works from Hanyang University: For example:

Picture of finite baryon density systems 5d gravity 4d gauge theory curved geometry (negative curvature) baryon charge Electric field A 0 : electric potential Baryon chemical potential No such an “electric field” in QCD.

We can investigate the phase structure of gauge theories T μ free quarks quark bound states (mesons) The details are still under investigation.

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 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.) talks given by Prof. Sin and Dr. Y. Kim

Old frameworks “Old” frameworks for macroscopic physics: Finite temperature, finite density: Thermodynamics (Boltzmann, Gibbs,….) If we add time-dependence further: Hydrodynamics (Landau, ….) Static but non-equilibrium cases: Linear response theory (Kubo, ….) equilibrium, static local equilibrium, slightly non-static 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: superstring theory general relativity quantum field theory hydrodynamics thermodynamics and statistical mechanics linear response theory Many beautiful toys are in the same box!

The gauge/gravity duality Highly non-equilibrium systems Highly dissipative systems Small volume (mesoscopic) systems Highly entangled systems A new tool for analysis of QCD (strongly coupled gauge theories). We have also a chance to get a hint for: