AdS/CFT Duality User Guide

Abstract

This is the draft/updated version of a textbook on "real-world" applications of the AdS/CFT duality for beginning graduate students in particle physics and for researchers in the other fields. The aim of this book is to provide background materials such as string theory, general relativity, nuclear physics, nonequilibrium physics, and condensed-matter physics as well as some key applications of the AdS/CFT duality in a single textbook. Contents: (1) Introduction, (2) General relativity and black holes, (3) Black holes and thermodynamics, (4) Strong interaction and gauge theories, (5) The road to AdS/CFT, (6) The AdS spacetime, (7) AdS/CFT - equilibrium, (8) AdS/CFT - adding probes, (9) Basics of nonequilibrium physics, (10) AdS/CFT - nonequilibrium, (11) Other AdS spacetimes, (12) Applications to quark-gluon plasma, (13) Basics of phase transition, (14) AdS/CFT - phase transition, (15) Exercises.Comment: 309 pages. Comments welcome. Published edition is available from Springer (Lecture Notes in Physics 903). Translated from a Japanese book originally published in 2012; v2: various improvements; v3: minor corrections, v4: added materials & minor improvements after publication (see "Preface for the arXiv edition" for details). http://link.springer.com/book/10.1007/978-4-431-55441-

Models of phase stability in Jackiw-Teitelboim gravity

“…In order to do so, we choose a ρ = Const. hypersurface [55]. Let us now define an outward normal n ρ , pointing along the increasing ρ, as,…”

Non-equilibrium statistical approach to friction models

“…It is based on the geometry appearing in the system dynamics. In the text, the metric is obtained in (6) and (8) for the SB model and in (21) for the BK model.…”

Derivation of kernel of dynamic support vector machines: Stochastic and deterministic data process

“…In the context of AdS/CFT correspondence, diffusion equation and wave equation appear as a reflection of Fick's law [10,11,12]. The solutions of these equations are interpreted as kernel, described in former sections.…”