Vertex Operators for Irregular Conformal Blocks: Supersymmetric Case

TL;DR

This paper constructs supersymmetric irregular vertex operators of arbitrary rank, revealing their unique block-diagonal structure and connection to the Ramond sector, contrasting with the bosonic case.

Contribution

It introduces supersymmetric irregular vertex operators of arbitrary rank and analyzes their distinct block-diagonal structure, advancing understanding of supersymmetric conformal blocks.

Findings

Supersymmetric irregular vertices are not eigenstates but block-diagonalize Virasoro and W_N generators.

The structure relates to Ramond sector contributions in colliding limits.

Differences from bosonic irregular operators are significant and structurally distinct.

Abstract

We construct supersymmetric irregular vertex operators of arbitrary rank, appearing in the colliding limit of primary fields. We find that the structure of the supersymmetric irregular vertices differs significantly from the bosonic case: upon supersymmetrization, the irregular operators are no longer the eigenstates of positive Virasoro and $W_N$ generators but block-diagonalize them. We relate the block-diagonal structure of the irregular vertices to contributions of the Ramond sector to the colliding limit.