Seiberg-Witten prepotential for E-string theory and random partitions
Abstract
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.
- Publication:
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Journal of High Energy Physics
- Pub Date:
- June 2012
- DOI:
- 10.1007/JHEP06(2012)027
- arXiv:
- arXiv:1203.2921
- Bibcode:
- 2012JHEP...06..027S
- Keywords:
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- Differential and Algebraic Geometry;
- Topological Strings;
- High Energy Physics - Theory;
- Mathematics - Algebraic Geometry
- E-Print:
- 14 pages