Holographic currents in first order Gravity and finite Fefferman-Graham expansions

TL;DR

This paper explores holographic currents in Chern-Simons theories, deriving finite Fefferman-Graham expansions and boundary currents like stress tensor and spin current, confirming their Ward identities.

Contribution

It provides a new gauge fixing in five-dimensional Chern-Simons gravity that yields finite Fefferman-Graham expansions and explicitly constructs holographic boundary currents.

Findings

Holographic vector and chiral currents reproduce the chiral anomaly.

Finite Fefferman-Graham expansion achieved in 5D Chern-Simons gravity.

Derived boundary stress tensor and spin current satisfying Ward identities.

Abstract

We study the holographic currents associated to Chern-Simons theories. We start with an example in three dimensions and find the holographic representations of vector and chiral currents reproducing the correct expression for the chiral anomaly. In five dimensions, Chern-Simons theory for AdS group describes first order gravity and we show that there exists a gauge fixing leading to a finite Fefferman-Graham expansion. We derive the corresponding holographic currents, namely, the stress tensor and spin current which couple to the metric and torsional degrees of freedom at the boundary, respectively. We obtain the correct Ward identities for these currents by looking at the bulk constraint equations.