Exact four dimensional string solutions and Toda-like sigma models from `null-gauged' WZNW theories

TL;DR

This paper constructs exact four-dimensional string solutions using null-gauged WZNW models for rank 2 non-compact groups, resulting in conformal backgrounds with one time-like dimension and Toda-like sigma models.

Contribution

It introduces a novel null gauging method for WZNW models that yields exact string backgrounds with specific signatures and Toda model analogs, expanding the toolkit for string solution construction.

Findings

Constructed new exact 4D string solutions with specific signatures.

Demonstrated absence of alpha'-corrections in these backgrounds.

Linked the models to Toda-like sigma models with conformal invariance.

Abstract

We construct a new class of exact string solutions with a four dimensional target space metric of signature ($-,+,+,+$) by gauging the independent left and right nilpotent subgroups with `null' generators of WZNW models for rank 2 non-compact groups $G$. The `null' property of the generators (${\rm Tr }(N_n N_m)=0$) implies the consistency of the gauging and the absence of $\a'$-corrections to the semiclassical backgrounds obtained from the gauged WZNW models. In the case of the maximally non-compact groups ($G= SL(3), SO(2,2), SO(2,3), G_2$) the construction corresponds to gauging some of the subgroups generated by the nilpotent `step' operators in the Gauss decomposition. The rank 2 case is a particular example of a general construction leading to conformal backgrounds with one time-like direction. The conformal theories obtained by integrating out the gauge field can be considered as sigma model analogs of Toda models (their classical equations of motion are equivalent to Toda model equations). The procedure of `null gauging' applies also to other non-compact groups.