A new Rational Conformal Field Theory extension of the fully degenerate W_{1+\infty}^{(m)}

TL;DR

This paper introduces a new rational conformal field theory extension of the fully degenerate W_{1+infty}^{(m)} algebra, characterized by novel identities involving Dedekind eta-functions and algebra characters, expanding understanding of orbifold theories.

Contribution

It presents the first characterization of the Z_{m}-orbifold of free bosons as an extension of the degenerate W_{1+infty}^{(m)} algebra, establishing it as a Gamma_{theta}-RCFT.

Findings

Identified new identities among Dedekind eta-functions and algebra characters.

Characterized the Z_{m}-orbifold of free bosons as an extension of W_{1+infty}^{(m)}.

Proved the orbifold theory is a Gamma_{theta}-RCFT extension.

Abstract

We found new identities among the Dedekind eta-function, the characters of the W_{m} algebra and those of the level 1 affine Lie algebra su(m)_{1}. They allow to characterize the Z_{m}-orbifold of the m-component free bosons u(1)_{K_{m,p}} (our theory TM) as an extension of the fully degenerate representations of W_{1+infty}^{(m)}. In particular, TM is proven to be a Gamma _{theta}-RCFT extension of the chiral fully degenerate W_{1+infty}^{(m)}.