Nonlocal Matrix Generalizations of N=2 Super Virasoro Algebra

TL;DR

This paper extends the N=2 super Virasoro algebra through nonlocal matrix generalizations of the Gelfand-Dickey bracket, deriving a superalgebra that includes known structures and exploring its bosonic limit.

Contribution

It introduces a novel nonlocal, nonlinear N=2 superalgebra based on matrix-valued superdifferential operators, generalizing existing algebraic frameworks.

Findings

Derived a nonlocal, nonlinear N=2 superalgebra containing the super Virasoro algebra.

Established the bosonic limit and connected it to the $V_{2,2}$ algebra.

Provided the Miura transformation for this generalized algebra.

Abstract

We study the generalization of second Gelfand-Dickey bracket to the superdifferential operators with matrix-valued coefficients. The associated Miura transformation is derived. Using this bracket we work out a nonlocal and nonlinear N=2 superalgebra which contains the N=2 super Virasoro algebra as a subalgebra. The bosonic limit of this algebra is considered. We show that when the spin-1 fields in this bosonic algebra are set to zero the resulting Dirac bracket gives precisely the recently derived $V_{2,2}$ algebra.