Exact string backgrounds from WZW models based on non-semi-simple groups

TL;DR

This paper constructs exact string backgrounds using WZW models based on non-semi-simple groups, revealing new conformal field theories with specific symmetries and confirming their consistency through one-loop and exact calculations.

Contribution

It introduces a novel class of WZW models on extended Euclidean groups, providing explicit string backgrounds with null Killing vectors and matching one-loop and exact results.

Findings

Exact string backgrounds with null Killing vectors are obtained.

One-loop results match the exact solutions after parameter shifts.

New conformal field theories are identified from non-semi-simple group WZW models.

Abstract

We formulate WZW models based on a centrally extended version of the Euclidean group in $d$-dimensions. We obtain string backgrounds corresponding to conformal $\s$-models in $D=d^2$ space-time dimensions with exact central charge $c=d^2$ and $d(d-1)/2$ null Killing vectors. By identifying the corresponding conformal field theory we show that the one loop results coincide with the exact ones up to a shifting of a parameter.