Crystallographic Orbifolds: Towards a Classification of Unitary Conformal Field Theories with Central Charge c = 2

TL;DR

This paper classifies the moduli space of unitary 2D conformal field theories with central charge c=2, constructing and analyzing 28 orbifold components, and relating them to known theories and geometric interpretations.

Contribution

It explicitly constructs all nonexceptional orbifold components of the c=2 moduli space and connects them to toroidal theories and previous classifications.

Findings

28 nonexceptional orbifold components identified

Explicit parameter spaces and partition functions calculated

Most components connected to toroidal theories in C^2

Abstract

We study the moduli space C^2 of unitary two-dimensional conformal field theories with central charge c=2. We construct all the 28 nonexceptional nonisolated irreducible components of C^2 that may be obtained by an orbifold procedure from toroidal theories. The parameter spaces and partition functions are calculated explicitly, and all multicritical points and lines are determined. We show that all but four of the 28 irreducible components of C^2 corresponding to nonexceptional orbifolds are directly or indirectly connected to the moduli space of toroidal theories in C^2. We relate our results to those by Dixon, Ginsparg, Harvey on the classification of c=3/2 superconformal field theories and thereby give geometric interpretations to all nonisolated orbifolds discussed there.