Holographic Aspects of Even-Dimensional Topological Gravity

TL;DR

This paper explores the holographic properties of even-dimensional topological gravity derived from odd-dimensional Chern-Simons theories, analyzing boundary correlators and anomalies in a four-dimensional context.

Contribution

It introduces a novel approach to study holography in even-dimensional topological gravity obtained via dimensional reduction from Chern-Simons theories, including correlation functions and anomalies.

Findings

The spin-current can have a nonzero expectation value in the dual theory.

The holographic Weyl anomaly vanishes in this setup.

A method for computing two-point functions using gravitational Wilson lines is proposed.

Abstract

In an odd-dimensional spacetime, gravity can be formulated as a proper gauge theory based on the Chern-Simons action for a suitable gauge group. Performing dimensional reduction, one obtains, as an effective theory, Chamseddine's even-dimensional topological gravity with the reduced gauge symmetry. This theory involves a multiplet of scalar fields that appear as a result of the dimensional reduction, and it is topological in the sense that its action does not depend on the metric. Focusing primarily on the four-dimensional case, we use the holographic dictionary to compute one-point correlation functions of the relevant boundary operators and find that the spin-current can have a nonzero expectation value in the dual quantum field theory. We also consider the generalized holographic Weyl anomaly and find that it vanishes. Finally, we propose a way of computing two-point correlation functions using the gravitational Wilson lines.