Probing the Strong Coupling Limit of Large N SYM on Curved Backgrounds

TL;DR

This paper explores the strong coupling behavior of large N=4 SYM on curved backgrounds using AdS/CFT, focusing on black hole geometries and Wilson loop properties, revealing thermal stabilization and phase transition insights.

Contribution

It investigates the strong coupling limit of large N=4 SYM on curved backgrounds, analyzing black hole solutions and Wilson loop behavior, including thermal stabilization and phase transition distinctions.

Findings

Thermal stabilization observed in hyperbolic black hole backgrounds.

Wilson loop screening length analyzed at finite temperature.

Sphere phase transition is unrelated to screening phenomena.

Abstract

According to the AdS/CFT correspondence, the strong coupling limit of large n, N=4 supersymmetric gauge theory at finite temperature is described by asymptotically anti de Sitter black holes. These black holes exist with planar, spherical and hyperbolic horizon geometries. We concentrate on the hyperbolic and spherical cases and probe the associated gauge theories with D3-branes and Wilson loops. The D3-brane probe reproduces the coupling of the scalars in the gauge theory to the background geometry and we find thermal stabilization in the hyperbolic case. We investigate the vacuum expectation value of Wilson loops with particular emphasis on the screening length at finite temperature. We find that the thermal phase transition of the theory on the sphere is not related to screening phenomena.