The Holomorphic Anomaly of Topological Strings

TL;DR

This paper demonstrates that the BRS operator in the topological string B model is not holomorphic, challenging the traditional interpretation of the holomorphic anomaly as a BRS anomaly.

Contribution

It clarifies the nature of the holomorphic anomaly in topological strings, showing it is not due to a BRS anomaly, which refines the theoretical understanding.

Findings

BRS operator is not holomorphic in the complex structure.

Holomorphic anomaly should not be viewed as a BRS anomaly.

Provides new insight into the mathematical structure of topological strings.

Abstract

We show that the BRS operator of the topological string B model is not holomorphic in the complex structure of the target space. This implies that the so-called holomorphic anomaly of topological strings should not be interpreted as a BRS anomaly.