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arXiv · 2211.07251

More on Seiberg-Witten Theory and Monstrous Moonshine

Shun'ya Mizoguchi·Takumi Oikawa·Hitomi Tashiro·Shotaro Yata
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Abstract

We continue the study of a relationship between the instanton expansion of the Seiberg-Witten (SW) prepotential of $D = 4$, ${\cal N }= 2$ $SU(2)$ SUSY gauge theory and the monstrous moonshine. Extending the previous results, we show for the cases of $N_f=2$ and $3$ that $q=e^{2πiτ}$, where $τ$ is the complex gauge coupling, again has an expansion whose coefficients are all integer-coefficient polynomials of the moonshine coefficients of the modular $j$-function in terms of an appropriate expansion variable. We also demonstrate that the new method of calculating the SW prepotential developed here is useful by performing some explicit computations.

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Shun'ya Mizoguchi, Takumi Oikawa, Hitomi Tashiro, Shotaro Yata. 2022-12-10. More on Seiberg-Witten Theory and Monstrous Moonshine. https://arxiv.org/abs/2211.07251

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