The abelian cosets of the Heisenberg group

TL;DR

This paper analyzes abelian cosets of the H(4) WZW model, revealing their connections to various three-dimensional backgrounds and providing detailed conformal field theory characterizations and couplings.

Contribution

It offers a comprehensive CFT analysis of abelian cosets of H(4), including character computations and coupling evaluations, linking them to known 3D geometries.

Findings

Identified relations between cosets and 3D backgrounds like Melvin models and orbifolds.

Computed coset characters and three-point couplings.

Established connections to interesting geometric models.

Abstract

In this paper we study the abelian cosets of the H(4) WZW model. They coincide or are related to several interesting three-dimensional backgrounds such as the Melvin model, the conical point-particle space-times and the null orbifold. We perform a detailed CFT analysis of all the models and compute the coset characters as well as some typical three-point couplings of coset primaries.