Seiberg-Witten prepotential for E-string theory and random partitions

Details Seiberg-Witten prepotential for E-string theory and random partitions Seiberg-Witten prepotential for E-string theory and random partitions

2012-03-13

arxiv.org/abs/1203.2921v1

Physics

High Energy Physics

High Energy Physics - Theory

14 pages

Scientific paper

We find a Nekrasov-type expression for the Seiberg-Witten prepotential for the six-dimensional non-critical E_8 string theory toroidally compactified down to four dimensions. The prepotential represents the BPS partition function of the E_8 strings wound around one of the circles of the toroidal compactification with general winding numbers and momenta. We show that our expression exhibits expected modular properties. In particular, we prove that it obeys the modular anomaly equation known to be satisfied by the prepotential.

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