Generalised Virasoro Constructions from Affine Inonu-Wigner Contractions

TL;DR

This paper introduces a novel method for deriving Virasoro algebra solutions from affine Lie algebras using Inönü-Wigner contractions, enabling the construction of multi-parameter Virasoro models, including generalizations of known cases.

Contribution

The authors develop a perturbative approach to extend Virasoro constructions from contracted affine Lie algebras to original algebras, broadening the scope of possible solutions.

Findings

Derived fixed-level multi-parameter Virasoro constructions for orthogonal algebras.

Extended Virasoro constructions from contracted algebras to original algebras.

Generalized the one-parameter Virasoro construction of 9(2) at level four.

Abstract

We present a new method to find solutions of the Virasoro master equations for any affine Lie algebra $\widehat{g}$. The basic idea is to consider first the simplified case of an In\"on\"u-Wigner contraction $\widehat{g}_c$ of $\widehat{g}$ and to extend the Virasoro constructions of $\widehat{g}_c$ to $\widehat{g}$ by a perturbative expansion in the contraction parameter. The method is then applied to the orthogonal algebras, leading to fixed-level multi-parameter Virasoro constructions, which are the generalisations of the one-parameter Virasoro construction of $\widehat{su}(2)$ at level four.