The W(sl(N+3),sl(3)) algebras and their contractions to W3

TL;DR

This paper constructs nonlinear W-algebras related to sl(N+3) and sl(3), explores their contraction to W3, and provides new insights into their central charge spectrum and realizations.

Contribution

It introduces the construction of W(sl(N+3),sl(3)) algebras, analyzes their contraction to W3, and offers new predictions for the central charge spectrum in minimal models.

Findings

Spectrum of central charges for contractions to W3 identified

New realizations of W3 constructed via linearization

Part of the central charge spectrum is newly determined

Abstract

We construct the nonlinear $W(sl(N+3),sl(3))$ algebras and find the spectrum of values of the central charge that gives rise, by contracting the $W(sl(N+3),sl(3))$ algebras, to a $W_3$ algebra belonging to the coset $W((sl(N+3),sl(3))/(u(1)\oplus sl(N))$. Part of the spectrum was conjectured before, but part of it is given here for the first time. Using the tool of embedding the $W(sl(N+3),sl(3))$ algebras into linearizing algebras, we construct new realizations of $W_3$ modulo null fields. The possibility to predict, within the conformal linearization framework, the central charge spectrum for minimal models of the nonlinear $W(sl(N+3),sl(3))$ algebras is discussed at the end.