Thermodynamic limit of the Nekrasov-type formula for E-string theory

Abstract

We give a proof of the Nekrasov-type formula proposed by one of the authors for the Seiberg-Witten prepotential for the E-string theory on R^4 x T^2. We take the thermodynamic limit of the Nekrasov-type formula following the example of Nekrasov-Okounkov and reproduce the Seiberg-Witten description of the prepotential. The Seiberg-Witten curve obtained directly from the Nekrasov-type formula is of genus greater than one. We find that this curve is transformed into the known elliptic curve by a simple map. We consider the cases in which the low energy theory has E_8, E_7+A_1 or E_6+A_2 as a global symmetry.

19 pages. v2: title and footnote 1 changed, typos corrected, version to appear in JHEP

References in corpus (3)

• Webs of five-branes and N=2 superconformal field theories
• Refined stable pair invariants for E-, M- and [p,q]-strings
• Topological strings and 5d T_N partition functions

Cited by in corpus (8)

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• Tao Probing the End of the World
• On the Elliptic Genus of Three E-strings and Heterotic Strings
• Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
• A reduced BPS index of E-strings
• M-strings in thermodynamic limit: Seiberg-Witten geometry
• E-strings, $F_4$, and $D_4$ triality
• Comments on the Nekrasov-type formula for E-string theory