Chern-Simons Gravity, Wilson Lines and Large N Dual Gauge Theories

TL;DR

This paper explores a five-dimensional Chern-Simons gravity model based on SO(4,2), revealing insights into holography, boundary conformal geometry, and dual gauge theories through Wilson line analysis and thermodynamic matching.

Contribution

It introduces a Chern-Simons gravity framework for AdS space that connects boundary conformal invariance with dual gauge theory properties, including Wilson line factorization.

Findings

Thermodynamic quantities relate coupling constants to dual field content.

Wilson line factorization in gravity induces dual observable factorization.

Conformal geometry naturally emerges as a boundary gauge invariance.

Abstract

A five-dimensional Chern-Simons gravity theory based on the anti-de Sitter group SO(4,2) is argued to be a useful model in which to understand the details of holography and the relationship between generally covariant and dual local quantum field theories. Defined on a manifold with boundary, conformal geometry arises naturally as a gauge invariance preserving boundary condition. By matching thermodynamic quantities for a particular background geometry, the dimensionless coupling constant of the Chern-Simons theory is directly related to the number of fields in a putative dual theory at high temperature. As a consistency check, the semiclassical factorization of Wilson line observables in the gravity theory is shown to induce a factorization in dual theory observables as expected by general arguments of large N gauge theory.