Generalized N=2 Topological Amplitudes and Holomorphic Anomaly Equation

TL;DR

This paper extends the understanding of N=2 topological amplitudes in string theory, revealing their broader class at higher loops and deriving associated anomaly equations influenced by supersymmetry and boundary effects.

Contribution

It demonstrates that a previously studied class of N=2 topological amplitudes is a special case of a more general set appearing at higher loops, and derives their anomaly equations.

Findings

The class of amplitudes is a subset of more general higher-loop amplitudes.

Derived differential equations from supersymmetry Ward identities.

Proved the anomaly equations are integrable and form a closed set.

Abstract

In arXiv:0905.3629 we described a new class of N=2 topological amplitudes that depends both on vector and hypermultiplet moduli. Here we find that this class is actually a particular case of much more general topological amplitudes which appear at higher loops in heterotic string theory compactified on K3 x T^2. We analyze their effective field theory interpretation and derive particular (first order) differential equations as a consequence of supersymmetry Ward identities and the 1/2-BPS nature of the corresponding effective action terms. In string theory the latter get modified due to anomalous world-sheet boundary contributions, generalizing in a non-trivial way the familiar holomorphic and harmonicity anomalies studied in the past. We prove by direct computation that the subclass of topological amplitudes studied in arXiv:0905.3629 forms a closed set under these anomaly equations and that these equations are integrable.