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arXiv · 1510.09060

Irregular conformal block, spectral curve and flow equations

Sang Kwan Choi·Chaiho Rim·Hong Zhang
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Abstract

Irregular conformal block is motivated by the Argyres-Douglas type of N=2 super conformal gauge theory. We investigate the classical/NS limit of the irregular conformal block using spectral curve on a Riemann surface with irregular punctures, which is equivalent to the loop equation of irregular matrix model. The spectral curve is reduced to the second order (Virasoro symmetry, $SU(2)$ for the gauge theory) and third order ($W_3$ symmetry, $SU(3)$) differential equations of a polynomial with finite degree. The Virasoro and W symmetry generate flow equations in the spectral curve and determine the irregular conformal block, hence the partition function of the Argyres-Douglas theory ala AGT conjecture.

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Sang Kwan Choi, Chaiho Rim, Hong Zhang. 2016-03-04. Irregular conformal block, spectral curve and flow equations. https://doi.org/10.1007/jhep03(2016)118

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