Quantum Matrix Models for Simple Current Orbifolds

TL;DR

This paper develops an algebraic approach to stringy geometry on simple current orbifolds of WZW models using Reflection Equation Algebras, connecting algebraic automorphisms with conformal field theory data.

Contribution

It introduces a novel algebraic formulation of orbifold models via REA_q(A_N), linking algebra automorphisms with CFT properties and providing new insights into brane tensions.

Findings

REA_q(A_N) shares automorphisms with current algebra A^{(1)}_N

Orbifold matrix models match BCFT data on brane tensions

Algebraic framework naturally encodes CFT monodromy charge

Abstract

An algebraic formulation of the stringy geometry on simple current orbifolds of the WZW models of type A_N is developed within the framework of Reflection Equation Algebras, REA_q(A_N). It is demonstrated that REA_q(A_N) has the same set of outer automorphisms as the corresponding current algebra A^{(1)}_N which is crucial for the orbifold construction. The CFT monodromy charge is naturally identified within the algebraic framework. The ensuing orbifold matrix models are shown to yield results on brane tensions and the algebra of functions in agreement with the exact BCFT data.