More on counterterms in the gravitational action and anomalies

TL;DR

This paper discusses how adding boundary counterterms to the gravitational action in asymptotically anti-de Sitter spacetimes helps define the partition function unambiguously, especially when p-form fields and matter-induced anomalies are involved.

Contribution

It explicitly identifies additional counterterms needed for p-form fields and relates matter field divergences to conformal anomalies, matching predictions for superconformal theories.

Findings

Counterterms for p-form fields are explicitly identified.

Logarithmic divergences relate to conformal anomalies.

Anomaly predictions agree with superconformal SU(N) gauge theory.

Abstract

The addition of boundary counterterms to the gravitational action of asymptotically anti-de Sitter spacetimes permits us to define the partition function unambiguously without background subtraction. We show that the inclusion of p-form fields in the gravitational action requires the addition of further counterterms which we explicitly identify. We also relate logarithmic divergences in the action dependent on the matter fields to anomalies in the dual conformal field theories. In particular we find that the anomaly predicted for the correlator of the stress energy tensor and two vector currents in four dimensions agrees with that of the ${\cal{N}} = 4$ superconformal SU(N) gauge theory.