Modular Anomaly from Holomorphic Anomaly in Mass Deformed N=2 Superconformal Field Theories

TL;DR

This paper investigates the relationship between modular and holomorphic anomalies in mass-deformed superconformal field theories, providing universal formulas and demonstrating SL(2,Z) duality invariance of the partition functions.

Contribution

It offers a clear resolution to the longstanding puzzle of the relation between modular and holomorphic anomalies, introducing universal formulas and analyzing duality invariance.

Findings

Partition functions are invariant under SL(2,Z) duality.

Derived universal formulas linking anomalies.

Resolved the relation between modular and holomorphic anomalies.

Abstract

We study the instanton partition functions of two well-known superconformal field theories with mass deformations. Two types of anomaly equations, namely, the modular anomaly and holomorphic anomaly, have been discovered in the literature. We provide a clean solution to the long standing puzzle about their precise relation, and obtain some universal formulas. We show that the partition function is invariant under the SL(2,Z) duality which exchanges theories at strong coupling with those of weak coupling.