Formula for Fixed Point Resolution Matrix of Permutation Orbifolds

TL;DR

This paper derives a formula for resolving fixed points in permutation orbifold conformal field theories extended by simple currents, ensuring the resulting S matrix is unitary and modular invariant.

Contribution

It provides a new explicit formula for fixed point resolution in permutation orbifold CFTs with simple current extensions, enhancing understanding of their modular properties.

Findings

Derived a formula for fixed point resolution in permutation orbifolds.

Proved the resulting S matrix is unitary and modular invariant.

Applicable to theories extended by (half-)integer spin simple currents.

Abstract

We find a formula for the resolution of fixed points in extensions of permutation orbifold conformal field theories by its (half-)integer spin simple currents. We show that the formula gives a unitary and modular invariant S matrix.