New Duality Transformations in Orbifold Theory

TL;DR

This paper introduces new duality transformations that enable the construction of stress tensors for all twisted sectors in orbifold conformal field theories, broadening the understanding of their structure and symmetries.

Contribution

The paper develops a general formalism for duality transformations in orbifold theories, including permutation orbifolds, and connects these to solutions of the orbifold Virasoro master equation.

Findings

Constructed stress tensors for twisted sectors in orbifold theories.

Illustrated the formalism with permutation orbifolds H=Z_λ and H=S_3.

Linked duality transformations to solutions of the orbifold Virasoro master equation.

Abstract

We find new duality transformations which allow us to construct the stress tensors of all the twisted sectors of any orbifold A(H)/H, where A(H) is the set of all current-algebraic conformal field theories with a finite symmetry group H \subset Aut(g). The permutation orbifolds with H = Z_\lambda and H = S_3 are worked out in full as illustrations but the general formalism includes both simple and semisimple g. The motivation for this development is the recently-discovered orbifold Virasoro master equation, whose solutions are identified by the duality transformations as sectors of the permutation orbifolds A(D_\lambda)/Z_\lambda.