The Wald entropy and 6d conformal anomaly

TL;DR

This paper investigates how different forms of the 6-dimensional conformal anomaly affect the Wald entropy, especially focusing on total derivative terms and their impact on conformal invariance and holographic calculations.

Contribution

It provides a detailed analysis of the Wald entropy's dependence on total derivative terms in the 6d conformal anomaly and clarifies the origin of the Hung-Myers-Smolkin discrepancy.

Findings

Wald entropy varies with different anomaly forms due to total derivative terms.

Total derivative terms break conformal invariance of the Wald entropy.

The discrepancy in holographic calculations is explained by these total derivative contributions.

Abstract

We analyze the Wald entropy for different forms of the conformal anomaly in six dimensions. In particular we focus on the anomaly which arises in a holographic calculation of Henningson and Skenderis. The various presentations of the anomaly differ by some total derivative terms. We calculate the corresponding Wald entropy for surfaces which do not have an Abelian $O(2)$ symmetry in the transverse direction although the extrinsic curvature vanishes. We demonstrate that for this class of surfaces the Wald entropy is different for different forms of the conformal anomaly. The difference is due to the total derivative terms which are present in the anomaly. We analyze the conformal invariance of the Wald entropy for the holographic conformal anomaly and demonstrate that the violation of the invariance is due to the contributions of the total derivative terms in the anomaly. Finally, we make more precise general form of the Hung-Myers-Smolkin discrepancy.