Exact string background from a WZW model based on the Heisenberg group

TL;DR

This paper constructs a WZW model based on the Heisenberg group, revealing a corresponding D-dimensional plane-wave string background with Lorentzian signature and an integer central charge, advancing understanding of non-semi-simple group models.

Contribution

It introduces a new WZW model for the Heisenberg group, generalizing previous models and linking it to specific string backgrounds with Lorentzian signature.

Findings

The model corresponds to a D-dimensional plane-wave background.

The central charge of the model is an integer c=D.

The model extends the class of exact string backgrounds.

Abstract

A WZW model for the non-semi-simple D-dimensional Heisenberg group, which directly generalizes the E_{2}^{c} group, is constructed. It is found to correspond to an D-dimensional string background of plane-wave type with physical Lorentz signature D-2. Perturbative and non-perturbative considerations lead both to an integer central charge c=D.