Permutation Orbifold of N=2 Supersymmetric Minimal Models

TL;DR

This paper explores permutation orbifold conformal field theories applied to N=2 supersymmetric minimal models, revealing new structures and exceptional simple currents, and provides complete data for specific orbifolds.

Contribution

It introduces a novel analysis of permutation orbifolds in N=2 minimal models, uncovering unexpected simple currents and resolving fixed points, expanding the understanding of these theories.

Findings

Discovery of new structures relating different conformal field theories.

Identification of exceptional simple currents from off-diagonal fields.

Complete determination of CFT data with fixed point resolution for specific orbifolds.

Abstract

In this paper we apply the previously derived formalism of permutation orbifold conformal field theories to N=2 supersymmetric minimal models. By interchanging extensions and permutations of the factors we find a very interesting structure relating various conformal field theories that seems not to be known in literature. Moreover, unexpected exceptional simple currents arise in the extended permuted models, coming from off-diagonal fields. In a few situations they admit fixed points that must be resolved. We determine the complete CFT data with all fixed point resolution matrices for all simple currents of all Z_2-permutations orbifolds of all minimal N=2 models with k\neq 2 mod 4.