Whittaker pairs for the Virasoro algebra and the Gaiotto - BMT states

TL;DR

This paper studies Whittaker modules for specific subalgebras of the Virasoro algebra, providing structure theorems and explicit constructions of Gaiotto and BMT states within Virasoro Verma modules.

Contribution

It introduces new structure theorems for Whittaker modules related to particular Virasoro subalgebras and explicitly constructs Gaiotto and BMT states in arbitrary Virasoro Verma modules.

Findings

Structure theorems for universal Whittaker modules

Explicit construction of Gaiotto states

Explicit construction of BMT states

Abstract

In this paper we analyze Whittaker modules for two families of Wittaker pairs related to the subalgebras of the Virasoro algebra generated by L_r,..., L_{2r} and L_1,L_n. The structure theorems for the corresponding universal Whittaker modules are proved and some of their consequences are derived. All the Gaiotto {arXiv:0908.0307} and the Bonelli-Maruyoshi-Tanzini {arXiv:1112.1691} states in an arbitrary Virasoro algebra Verma module are explicitly constructed.