Super-spectral curve of irregular conformal blocks

TL;DR

This paper introduces a super-spectral curve approach to analyze irregular conformal blocks in supersymmetric models, revealing integrability and explicit partition functions for different sectors.

Contribution

It develops a super-spectral curve framework for irregular conformal states, connecting supersymmetric matrix models with conformal blocks and providing explicit partition functions.

Findings

Spectral curve is integrable at Nekrasov-Shatashvili limit.

Partition functions are explicitly derived for NS and Ramond sectors.

Super-spectral curve captures irregular conformal states in supersymmetric theories.

Abstract

We use super-spectral curve to investigate irregular conformal states of integer and half-odd integer rank. The spectral curve is the loop equation of supersymmetrized irregular matrix model. The case of integer rank corresponds to the colliding limit of supersymmetric vertex operators of NS sector and half-odd integer to the Ramond sectors. The spectral curve is simply integrable at Nekrasov-Shatashvili limit and the partition function (inner product of irregular conformal state) is obtained from the superconformal structure manifest in the spectral curve. We present some explicit forms of the partition function of integer (NS sector) and of half-odd ranks (Ramond sector).