Seiberg-Witten Theory and Monstrous Moonshine
Shun'ya Mizoguchi

TL;DR
This paper reveals a deep connection between the instanton expansion coefficients of Seiberg-Witten theory for certain supersymmetric gauge theories and the coefficients of the monstrous moonshine modular functions, suggesting a link between gauge theory and moonshine phenomena.
Contribution
It introduces a simple method to compute the Seiberg-Witten prepotential and demonstrates that its expansion coefficients relate to moonshine coefficients, bridging gauge theory and moonshine.
Findings
Coefficients are integer polynomials of moonshine coefficients.
Established a link between Seiberg-Witten theory and monstrous moonshine.
Suggested a relationship between Liouville CFT and moonshine module CFT.
Abstract
We study the relation between the instanton expansion of the Seiberg-Witten prepotential for , SUSY gauge theory for and and the monstrous moonshine. By utilizing a newly developed simple method to obtain the SW prepotential, it is shown that the coefficients of the expansion of in terms of () or () are all integer coefficient polynomials of the moonshine coefficients of the modular -function. A relationship between the AGT Liouville CFT and the vertex operator algebra CFT of the moonshine module is also suggested.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Particle physics theoretical and experimental studies · Quantum Chromodynamics and Particle Interactions
