论文标题
Seiberg-Witten理论和可怕的月光
Seiberg-Witten Theory and Monstrous Moonshine
论文作者
论文摘要
我们研究了$ d = 4 $，$ {\ cal n} = 2 $ $ su（2）$ n_f = 0 $和$ 1 $的instanton扩展的关系之间的关系。通过利用一种新开发的简单方法获得SW预势，可以表明，$ q = e^{2πτ} $的扩展系数在$ a^2 = \ frac {λ^2} {λ^2} {16 a^2} {16 a^2} $（$ n_f = 0 $ n_f = 0 $）或$ \ frac {2} （$ n_f = 1 $）都是模块化$ j $ function的月光系数的整数系数多项式。还建议在月光模块的AGT $ C = 25 $ LIOUVILE CFT与$ C = 24 $顶点操作员代数CFT之间的关系。
We study the relation between the instanton expansion of the Seiberg-Witten prepotential for $D=4$, ${\cal N}=2$ $SU(2)$ SUSY gauge theory for $N_f=0$ and $1$ 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 $q=e^{2πτ}$ in terms of $A^2=\frac{Λ^2}{16 a^2}$ ($N_f=0$) or $\frac{Λ^2}{16 \sqrt{2}a^2}$ ($N_f=1$) are all integer coefficient polynomials of the moonshine coefficients of the modular $j$-function. A relationship between the AGT $c = 25$ Liouville CFT and the $c = 24$ vertex operator algebra CFT of the moonshine module is also suggested.
