New Anomalies in Topological String Theory

TL;DR

This paper uncovers new anomalies in the topological string partition function with D-branes on compact Calabi-Yau manifolds, affecting the holomorphic anomaly equation and linking to BPS state counting in M-theory.

Contribution

It identifies novel anomalies that disrupt the recursive structure of the holomorphic anomaly equation and explains their microscopic origin, relating to recent BPS state counting results.

Findings

New anomalies spoil the holomorphic anomaly recursion.

Dependence on wrong moduli arises unless disk one-point functions vanish.

Provides a microscopic explanation for BPS state counting in M-theory.

Abstract

We show that the topological string partition function with D-branes on a compact Calabi-Yau manifold has new anomalies that spoil the recursive structure of the holomorphic anomaly equation and introduce dependence on wrong moduli (such as complex structure moduli in the A-model), unless the disk one-point functions vanish. This provides a microscopic explanation for the recent result of Walcher in arXiv:0712.2775 on counting of BPS states in M-theory using the topological string partition function. The relevance of vanishing disk one-point functions to large $N$ duality for compact Calabi-Yau manifolds is noted.