Automorphic instanton partition functions on Calabi-Yau threefolds
Paper in proceedings, 2012

We survey recent results on quantum corrections to the hypermultiplet moduli space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or, equivalently, the vector multiplet moduli space in type IIB/A on X × S 1. Our main focus lies on the problem of resumming the infinite series of D-brane and NS5-brane instantons, using the mathematical machinery of automorphic forms. We review the proposal that when the theory in three dimensions exhibits an arithmetic "U-duality" symmetry G(ℤ) the total instanton partition function arises from a certain unitary automorphic representation of G, whose Fourier coefficients reproduce the BPS-degeneracies. In the case of four-dimensional N = 2 theories on ℝ × S 1 we argue that the relevant automorphic representation falls in the quaternionic discrete series of G, and that the partition function is a holomorphic section on the twistor space Z over M.

Author

Daniel Persson

Chalmers, Applied Physics, Mathematical Physics

Journal of Physics: Conference Series

17426588 (ISSN) 17426596 (eISSN)

Vol. 346 1 Art. no. 012016-

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Other Physics Topics

DOI

10.1088/1742-6596/346/1/012016

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Created

10/7/2017