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

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

2. 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.

3. However, there are technical difficulties in the computations of: • time dependent systems • systems at finite baryon chemical potential • systems of large size 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.

4. 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.

5. AdS/CFT: a “holography” 4d gauge theory 5d gravity curved geometry (negative curvature)

6. 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?

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

8. 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

9. 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 Picture of time-dependent systems collision of heavy nuclei 4d gauge theory 5d gravity Expanding quark-gluon plasma at the RHIC experiment

10. 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

11. Baryon chemical potential No such an “electric field” in QCD. Picture of finite baryon density systems 4d gauge theory 5d gravity baryon charge A0: electric potential Electric field curved geometry (negative curvature)

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

13. 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.) 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

14. 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

15. 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 ?).

16. Highly non-equilibrium systems • Highly dissipative systems • Small volume (mesoscopic) systems • Highly entangled systems • ………………. • of certain (supersymmetric) gauge theories. The gauge/gravity duality may be a good playground for inventinga new theory of: something going beyondthermodynamics, hydrodynamics, or linear response theory:

17. Many beautiful toys are in the same box! 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

18. 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