Generalized N=2 Topological Amplitudes and Holomorphic Anomaly Equation

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.

55 pages, 2 figures

References in corpus (4)

• Holomorphic Anomaly in Gauge Theories and Matrix Models
• 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

Cited by in corpus (7)

• The Omega deformed B-model for rigid N=2 theories
• M-strings, Elliptic Genera and N=4 String Amplitudes
• Worldsheet Realization of the Refined Topological String
• Non-Abelian Tensor Towers and (2,0) Superconformal Theories
• Modular anomaly equations in N=2* theories and their large-N limit
• BPS Saturated String Amplitudes: K3 Elliptic Genus and Igusa Cusp Form
• Probing the Moduli Dependence of Refined Topological Amplitudes