Large N Field Theories, String Theory and Gravity

TL;DR

This paper reviews the holographic correspondence linking string theory and field theories, emphasizing Anti-de Sitter space compactifications, and discusses its implications for gravity, black holes, and QCD.

Contribution

It provides a comprehensive overview of the AdS/CFT correspondence, including background, evidence, and applications across various theories and dimensions.

Findings

Evidence supports the holographic duality in classical and semiclassical regimes.

Connections between string compactifications and conformal field theories are elucidated.

Implications for black hole physics and QCD are discussed.

Abstract

We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N=4 supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and non-conformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.