A WZW model based on a non-semi-simple group

TL;DR

This paper introduces a conformal field theory based on a WZW model with a non-semi-simple group, modeling a four-dimensional Lorentzian spacetime with potential for new geometries through duality.

Contribution

It constructs a novel ungauged WZW model on a central extension of the Poincaré algebra that describes four-dimensional Minkowski space with exact central charge.

Findings

Models a 4D Lorentzian spacetime with conformal symmetry

Exact central charge of four matching Minkowski space

Potential for new geometries via $O(3,3)$ duality

Abstract

We present a conformal field theory which desribes a homogeneous four dimensional Lorentz-signature space-time. The model is an ungauged WZW model based on a central extension of the Poincar\'e algebra. The central charge of this theory is exactly four, just like four dimensional Minkowski space. The model can be interpreted as a four dimensional monochromatic plane wave. As there are three commuting isometries, other interesting geometries are expected to emerge via $O(3,3)$ duality.