More About All Current-Algebraic Orbifolds

TL;DR

This paper extends the mode formulation and analysis of current-algebraic orbifolds, providing explicit constructions for twisted sectors, correlators, and weights, with detailed examples including permutation and inner-automorphic orbifolds.

Contribution

It introduces a comprehensive mode formulation for all sectors of current-algebraic orbifolds, including twisted currents, Virasoro generators, and correlators, expanding previous constructions.

Findings

Mode formulation for twisted sectors derived

Explicit expressions for twisted correlators obtained

Detailed examples of permutation and inner-automorphic orbifolds provided

Abstract

Recently a construction was given for the stress tensors of all sectors of the general current-algebraic orbifold A(H)/H, where A(H) is any current-algebraic conformal field theory with a finite symmetry group H. Here we extend and further analyze this construction to obtain the mode formulation of each sector of each orbifold A(H)/H, including the twisted current algebra, the Virasoro generators, the orbifold adjoint operation and the commutator of the Virasoro generators with the modes of the twisted currents. As applications, general expressions are obtained for the twisted current-current correlator and ground state conformal weight of each twisted sector of any permutation orbifold A(H)/H, H \subset S_N. Systematics are also outlined for the orbifolds A(Lie h(H))/H of the (H and Lie h)-invariant conformal field theories, which include the general WZW orbifold and the general coset orbifold. Finally, two new large examples are worked out in further detail: the general S_N permutation orbifold A(S_N)/S_N and the general inner-automorphic orbifold A(H(d))/H(d).