Negative Generators of the Virasoro Constraints for the BKP Hierarchy

TL;DR

This paper derives the string equation and Virasoro constraints for the BKP hierarchy's tau function using special symmetry flows, providing explicit forms of these flows and generators.

Contribution

It offers a straightforward derivation of Virasoro constraints for the BKP hierarchy and explicitly describes the symmetry flows and generators involved.

Findings

Explicit forms of additional symmetry flows on the wave function

Derivation of negative Virasoro generators $L_{-k}$

Connection between symmetry flows and Virasoro constraints

Abstract

We give a straightforward derivation of the string equation and Virasoro constraints on the $\tau$ function of the BKP hierarchy by means of some special additional symmetry flows. The explicit forms of the actions of these additional symmetry flows on the wave function and then the negative Virasoro generators $L_{-k}$ are given, where $k$ is a positive integer.