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.

14 pages

References in corpus (1)

• Matrix Models, Geometric Engineering and Elliptic Genera

Cited by in corpus (8)

• M-Strings
• Tao Probing the End of the World
• Measurement of the Cross-Correlation Angular Power Spectrum Between the Stochastic Gravitational Wave Background and Galaxy Over-Density
• Seiberg-Witten prepotential for E-string theory and global symmetries
• Thermodynamic limit of the Nekrasov-type formula for E-string theory
• A reduced BPS index of E-strings
• E-strings, $F_4$, and $D_4$ triality
• Comments on the Nekrasov-type formula for E-string theory