Conformally Invariant Path Integral Formulation of the Wess-Zumino-Witten $\to$ Liouville Reduction

Details Conformally Invariant Path Integral Formulation of the Wess-Zumino-Witten $\to$ Liouville Reduction Conformally Invariant Path Integral Formulation of the Wess-Zumino-Witten $\to$ Liouville Reduction

1997-09-19

arxiv.org/abs/hep-th/9709143v1

Nucl.Phys. B520 (1998) 513-532

Physics

High Energy Physics

High Energy Physics - Theory

Plain TeX file; 28 Pages

Scientific paper

10.1016/S0550-3213(98)00049-2

The path integral description of the Wess-Zumino-Witten $\to$ Liouville reduction is formulated in a manner that exhibits the conformal invariance explicitly at each stage of the reduction process. The description requires a conformally invariant generalization of the phase space path integral methods of Batalin, Fradkin, and Vilkovisky for systems with first class constraints. The conformal anomaly is incorporated in a natural way and a generalization of the Fradkin-Vilkovisky theorem regarding gauge independence is proved. This generalised formalism should apply to all conformally invariant reductions in all dimensions. A previous problem concerning the gauge dependence of the centre of the Virasoro algebra of the reduced theory is solved.

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