Conformal field theories in anti-de Sitter space

TL;DR

This paper explores how boundary conditions affect the dynamics of N=4 supersymmetric Yang-Mills theory on AdS_4, revealing phase transitions and dual gravitational descriptions depending on these conditions.

Contribution

It analyzes the impact of boundary conditions on the dynamics and phase structure of N=4 SYM on AdS_4, linking weak and strong coupling regimes via S-duality and AdS/CFT.

Findings

Boundary conditions significantly influence the phase behavior.

Certain boundary choices lead to known gravitational duals.

Phase structure varies with coupling and boundary conditions.

Abstract

In this paper we discuss the dynamics of conformal field theories on anti-de Sitter space, focussing on the special case of the N=4 supersymmetric Yang-Mills theory on AdS_4. We argue that the choice of boundary conditions, in particular for the gauge field, has a large effect on the dynamics. For example, for weak coupling, one of two natural choices of boundary conditions for the gauge field leads to a large N deconfinement phase transition as a function of the temperature, while the other does not. For boundary conditions that preserve supersymmetry, the strong coupling dynamics can be analyzed using S-duality (relevant for g_{YM} >> 1), utilizing results of Gaiotto and Witten, as well as by using the AdS/CFT correspondence (relevant for large N and large 't Hooft coupling). We argue that some very specific choices of boundary conditions lead to a simple dual gravitational description for this theory, while for most choices the gravitational dual is not known. In the cases where the gravitational dual is known, we discuss the phase structure at large 't Hooft coupling.