Irregular Vertex Operators for Irregular Conformal Blocks

TL;DR

This paper develops a free field representation for irregular vertex operators of any rank, enabling the construction of irregular coherent states and analysis of their correlation functions within conformal field theory.

Contribution

It introduces a novel free field framework for irregular vertex operators of arbitrary rank, expanding the understanding of irregular conformal blocks.

Findings

Constructed irregular vertex operators as exponentials of derivatives of Liouville/Toda fields.

Generated eigenstates of Virasoro and W symmetry modes.

Computed correlation functions and analyzed operator algebra.

Abstract

We construct the free field representation of irregular vertex operators of arbitrary rank which generates simultaneous eigenstates of positive modes of Virasoro and W symmetry generators. The irregular vertex operators turn out to be the exponentials of combinations of derivatives of Liouville or Toda fields, creating irregular coherent states. We compute examples of correlation functions of these operators and study their operator algebra.