Irregular Vertex Operators for Irregular Conformal Blocks

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.

17 pages, typos corrected, references and acknowledgements added

References in corpus (6)

• Asymptotically free N=2 theories and irregular conformal blocks
• Virasoro irregular conformal block and beta deformed random matrix model
• Irregular conformal block, spectral curve and flow equations
• Confluent primary fields in the conformal field theory
• Solutions in Bosonic String Field Theory and Higher Spin Algebras in AdS
• Irregular matrix model with $\mathcal{W}$ symmetry

Cited by in corpus (6)

• A slow review of the AGT correspondence
• Argyres-Douglas theories and Liouville Irregular States
• Vertex Operators for Irregular Conformal Blocks: Supersymmetric Case
• Irregular Conformal States and Spectral Curve: Irregular Matrix Model Approach
• Interactions of Irregular Gaiotto States in Liouville Theory
• Higher Spins as Rolling Tachyons in Open String Field Theory