Holographic Weyl anomaly in string theory

TL;DR

This paper calculates the worldsheet partition function for string theory in AdS3 with NS-NS flux, demonstrating it reproduces the holographic Weyl anomaly and clarifies the role of ambiguities related to boundary counterterms.

Contribution

It provides a direct worldsheet computation of the holographic Weyl anomaly in AdS3 string theory, linking worldsheet symmetries to boundary CFT properties.

Findings

Partition function reproduces the holographic Weyl anomaly.

Ambiguous terms correspond to boundary counterterms.

Cancellation of infinities due to M"obius symmetry.

Abstract

We compute the worldsheet sphere partition function of string theory on global AdS$_3$ with pure NS-NS flux. Because of an unfixed M\"obius symmetry on the worldsheet, there is a cancellation of infinities and only a part of the answer is unambiguous. We show that it precisely reproduces the holographic Weyl anomaly and the ambiguous terms correspond to the possible counterterms of the boundary CFT.