A New Class of N=2 Topological Amplitudes

TL;DR

This paper introduces a new class of N=2 topological amplitudes that compute specific BPS terms in supergravity, revealing their dependence on both vector and hypermultiplet moduli and analyzing their mathematical properties.

Contribution

It presents a novel class of topological amplitudes with moduli-dependent BPS terms, including their explicit conditions and boundary term analysis in heterotic string theory.

Findings

Amplitudes depend on vector and hypermultiplet moduli.

Holomorphicity and harmonicity conditions are satisfied up to boundary terms.

Obstructions to holomorphicity are linked to one-loop threshold corrections.

Abstract

We describe a new class of N=2 topological amplitudes that compute a particular class of BPS terms in the low energy effective supergravity action. Specifically they compute the coupling F^2(\lambda\lambda)^{g-2}(d\phi)^2 where F, \lambda and \phi are gauge field strengths, gaugino and holomorphic vector multiplet scalars. The novel feature of these terms is that they depend both on the vector and hypermultiplet moduli. The BPS nature of these terms implies that they satisfy a holomorphicity condition with respect to vector moduli and a harmonicity condition as well as a second order differential equation with respect to hypermultiplet moduli. We study these conditions explicitly in heterotic string theory and show that they are indeed satisfied up to anomalous boundary terms in the world-sheet moduli space. We also analyze the boundary terms in the holomorphicity and harmonicity equations at a generic point in the vector and hyper moduli space. In particular we show that the obstruction to the holomorphicity arises from the one loop threshold correction to the gauge couplings and we argue that this is due to the contribution of non-holomorphic couplings to the connected graphs via elimination of the auxiliary fields.