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.
Highlights
The dynamics of a scalar field has been studied in the WZW models and their gauged version, and the full spectrum of eigenvalues is known [2, 3].1 The construction of the relevant wavefunctions is a more complicated problem, and it has been solved only on a case-by-case basis [2, 3, 5]
We focus on the gauged WZW (gWZW) models which admit separation of variables in the Helmholtz equation for a scalar and demonstrate that separability of the vector equation in all such cases
The eigenvalues and eigenvectors of the scalar field on such background are known through the algebraic constructions [2, 3, 5],3 but it is not clear whether these algebraic methods can be extended to the vector field
Summary
The dynamics of a scalar field has been studied in the WZW models and their gauged version, and the full spectrum of eigenvalues is known [2, 3].1 The construction of the relevant wavefunctions is a more complicated problem, and it has been solved only on a case-by-case basis [2, 3, 5]. While these results are expected, at least for the scalar, since SO(4) = SU(2) × SU(2), and a metric on each SU(2) has only one non-cyclic direction, the detailed analysis of separability for the vector field reveals interesting structures which can be extended to the situations where separation of variables is less obvious.
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