Generalized N=2 Topological Amplitudes and Holomorphic Anomaly Equation

Article, Preprint English OPEN
Antoniadis, I. ; Hohenegger, S. ; Narain, K. S. ; Sokatchev, E. (2011)
  • Publisher: ELSEVIER SCIENCE BV
  • Journal: NUCLEAR PHYSICS B (issn: 0550-3213)
  • Related identifiers: doi: 10.1016/j.nuclphysb.2011.11.011
  • Subject: High Energy Physics - Theory
    arxiv: High Energy Physics::Theory

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.
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