Irregular Vertex Operators for Irregular Conformal Blocks

摘要

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