Chern-Simons Theories in the AdS/CFT Correspondence

TL;DR

The paper analyzes the AdS3/CFT2 correspondence for 3D theories with a Chern-Simons term, focusing on the Proca-Chern-Simons and Self-Dual models. Using holographic techniques, it derives the boundary two-point functions of the corresponding boundary currents, showing that the conformal dimensions are determined by the bulk masses and that the Maxwell-Chern-Simons limit reproduces the expected boundary data. It verifies the known equivalence between the Maxwell-Chern-Simons theory and the Self-Dual model by matching their boundary conformal dimensions when the bulk parameters satisfy the appropriate relation, and presents a universal form for the boundary data in terms of the bulk mass. The results highlight the holographic principle’s predictivity, with boundary correlators depending only on bulk mass parameters, independent of bulk details.

Abstract

We consider the AdS/CFT correspondence for theories with a Chern-Simons term in three dimensions. We find the two-point functions of the boundary conformal field theories for the Proca-Chern-Simons theory and the Self-Dual model. We also discuss particular limits where we find the two-point function of the boundary conformal field theory for the Maxwell-Chern-Simons theory. In particular our results are consistent with the equivalence between the Maxwell-Chern-Simons theory and the Self-Dual model.