The operator algebra of cyclic orbifolds

TL;DR

This paper characterizes the maximal chiral algebra of cyclic orbifolds, showing they are rational and diagonal if the original theory is, and computes fusion rules relevant for entanglement measures in critical systems.

Contribution

It identifies the maximal chiral algebra of cyclic orbifolds and demonstrates their rationality and diagonal structure under certain conditions, providing tools for operator analysis.

Findings

Maximal chiral algebra of cyclic orbifolds identified

Orbifolds are rational and diagonal if the mother theory is

Fusion rules computed via Verlinde formula

Abstract

We identify the maximal chiral algebra of conformal cyclic orbifolds. In terms of this extended algebra, the orbifold is a rational and diagonal conformal field theory, provided the mother theory itself is also rational and diagonal. The operator content and operator product expansion of the cyclic orbifolds are revisited in terms of this algebra. The fusion rules and fusion numbers are computed via the Verlinde formula. This allows one to predict which conformal blocks appear in a given four-point function of twisted or untwisted operators, which is relevant for the computation of various entanglement measures in one-dimensional critical systems.