Commuting quantities and exceptional W-algebras

TL;DR

This paper constructs commuting charges from U(1) Kac-Moody currents, linking them to exceptional W-algebras with specific central charges, revealing new algebraic structures in conformal field theory.

Contribution

It introduces a family of commuting charges associated with exceptional W-algebras for each positive integer n, expanding understanding of algebraic symmetries in conformal models.

Findings

Existence of sets S_n of commuting charges for each n > 1

Charges expressed in terms of generators of exceptional W-algebras

Central charge c = 13-6n-6/n in Feigin-Fuchs realization

Abstract

Sets of commuting charges constructed from the current of a U(1) Kac-Moody algebra are found. There exists a set S_n of such charges for each positive integer n > 1; the corresponding value of the central charge in the Feigin-Fuchs realization of the stress tensor is c = 13-6n-6/n. The charges in each series can be written in terms of the generators of an exceptional W-algebra.