Multilocal bosonization

TL;DR

This paper establishes a bilocal isomorphism linking a twisted boson field algebra with the boson βγ ghost system, revealing new symmetries and structures in vertex algebras.

Contribution

It introduces a novel bilocal isomorphism between twisted boson and ghost algebras, extending to multiple localization points and uncovering new algebraic symmetries.

Findings

Existence of untwisted and twisted Heisenberg currents in both algebras

Presence of three families of Virasoro fields

Generalization to algebras with multiple localization points

Abstract

We present a bilocal isomorphism between the algebra generated by a single real twisted boson field and the algebra of the boson $\beta\gamma$ ghost system. As a consequence of this twisted vertex algebra isomorphism we show that each of these two algebras possesses both an untwisted and a twisted Heisenberg bosonic currents, as well as three separate families of Virasoro fields. We show that this bilocal isomorphism generalizes to an isomorphism between the algebra generated by the twisted boson field with $2n$ points of localization and the algebra of the $2n$ symplectic bosons.