A New Class of N=2 Topological Amplitudes

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(λλ)^{g-2}(dϕ)^2 where F, λand ϕare 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.

70 pages

References in corpus (3)

• N=4 Topological Amplitudes and String Effective Action
• Harmonicity in N=4 supersymmetry and its quantum anomaly
• Topological Amplitudes and Physical Couplings in String Theory

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• $\mathcal{N}=2^{\star }$ from Topological Amplitudes in String Theory
• Probing the Moduli Dependence of Refined Topological Amplitudes
• Scattering of charged tensor bosons in gauge and superstring theories
• Generalized N=2 Topological Amplitudes and Holomorphic Anomaly Equation
• N=4 Topological Amplitudes and Black Hole Entropy
• One-loop Chern-Simons terms in five dimensions