Singular Contractions of W-algebras

TL;DR

This paper introduces a method to contract certain W-algebras at exceptional central charge values, resulting in new consistent degenerate algebras, expanding the understanding of their algebraic structure.

Contribution

It presents a novel contraction technique for W-algebras at special central charge values, revealing new degenerate algebra structures.

Findings

W-algebras are consistent except at discrete exceptional central charges

Contraction at these points yields new degenerate algebras

Expands the classification of W-algebra structures

Abstract

Many $W$-algebras (e.g. the $W_N$ algebras) are consistent for all values of the central charge except for a discrete set of exceptional values. We show that such algebras can be contracted to new consistent degenerate algebras at these exceptional values of the central charge.