Non-Local Virasoro Symmetries in the mKdV Hierarchy

TL;DR

This paper extends the dressing symmetry framework in the mKdV hierarchy, revealing non-local Virasoro algebra symmetries that may connect to deformed Virasoro algebra in 2D integrable field theories.

Contribution

It introduces a novel construction of non-local Virasoro symmetries in the mKdV hierarchy using vertex operators, suggesting a link to deformed Virasoro algebra.

Findings

Non-local Virasoro symmetries are constructed in the mKdV hierarchy.

The Virasoro algebra is realized through vertex operator expressions.

Potential connection to Deformed Virasoro Algebra in perturbed theories.

Abstract

We generalize the dressing symmetry construction in mKdV hierarchy. This leads to non-local vector fields (expressed in terms of vertex operators) closing a Virasoro algebra. We argue that this algebra realization should play an important role in the study of 2D integrable field theories and in particular should be related to the Deformed Virasoro Algebra (DVA) when the construction is perturbed out of the critical theory.