A Basic Class of Twisted Open WZW Strings

TL;DR

This paper extends the open-string WZW model to include twisted sectors, revealing new twisted non-commutative geometries and formulating associated quantum KZ equations, thereby enriching the understanding of open-string orbifolds.

Contribution

It introduces a comprehensive description of twisted open WZW strings, linking them to closed-string orbifolds and deriving their quantum twisted KZ equations.

Findings

Identification of twisted non-commutative geometries

Derivation of twisted open-string KZ equations

Connection between twisted open strings and closed-string orbifolds

Abstract

Recently, Giusto and Halpern reported the open-string description of a certain basic class of untwisted open WZW strings, including their associated non-commutative geometry and open-string KZ equations. In this paper, we combine this development with results from the theory of current-algebraic orbifolds to find the open-string description of a corresponding basic class of {\it twisted} open WZW strings, which begin and end on different WZW branes. The basic class of twisted open WZW strings is in 1-to-1 correspondence with the twisted sectors of all closed-string WZW orbifolds, and moreover, the basic class can be decomposed into a large collection of open-string WZW orbifolds. At the classical level, these open-string orbifolds exhibit new {\it twisted non-commutative geometries}, and we also find the relevant {\it twisted open-string KZ equations} which describe these orbifolds at the quantum level. In a related development, we also formulate the closed-string description (in terms of twisted boundary states) of the {\it general} twisted open WZW string.