Separation of variables in the WZW models

TL;DR

This paper demonstrates the full separation of variables for scalar and vector fields in certain WZW model backgrounds, revealing analogies with black hole geometries and extending to higher groups in specific cases.

Contribution

It provides a detailed analysis of variable separation in WZW models, highlighting new solvable cases for SO(4) and partial results for higher groups.

Findings

Full separation of variables for SO(4) models

Analogy with Myers-Perry black hole backgrounds

Partial separation in higher group models

Abstract

We consider dynamics of scalar and vector fields on gravitational backgrounds of the Wess-Zumino-Witten models. For SO(4) and its cosets, we demonstrate full separation of variables for all fields and find a close analogy with a similar separation of vector equations in the backgrounds of the Myers--Perry black holes. For SO(5) and higher groups separation of variables is found only in some subsectors.