Gauged W Algebras

TL;DR

This paper demonstrates how Hamiltonian reduction of classical extbackslash cw( extbackslash cg, extbackslash ch) algebras produces new extbackslash cw( extbackslash cg, extbackslash ch') algebras with extbackslash ch extbackslash subset extbackslash ch', especially for extbackslash cg=S extbackslash l(n), using the Generalized Horizontal Gauge.

Contribution

It establishes a method to relate different extbackslash cw-algebras via Hamiltonian reduction and a specific gauge choice, expanding understanding of their structure and interrelations.

Findings

Hamiltonian reduction yields new extbackslash cw-algebras with larger extbackslash ch'

Existence of Generalized Horizontal Gauge links extbackslash cw-algebras with nested extbackslash ch

Provides a systematic way to relate extbackslash cw-algebras through inclusion of extbackslash ch

Abstract

We perform an Hamiltonian reduction on a classical \cw(\cg, \ch) algebra, and prove that we get another \cw(\cg, \ch$'$) algebra, with $\ch\subset\ch'$. In the case $\cg=S\ell(n)$, the existence of a suitable gauge, called Generalized Horizontal Gauge, allows to relate in this way two \cw-algebras as soon as their corresponding \ch-algebras are related by inclusion.