Covariant $W$ Gravity \& its Moduli Space from Gauge Theory

Details Covariant $W$ Gravity \& its Moduli Space from Gauge Theory Covariant $W$ Gravity \& its Moduli Space from Gauge Theory

1992-06-25

arxiv.org/abs/hep-th/9206098v1

Nucl.Phys. B401 (1993) 369-412

Physics

High Energy Physics

High Energy Physics - Theory

52 pages, THU-92/14

Scientific paper

10.1016/0550-3213(93)90308-C

In this paper we study arbitrary $W$ algebras related to embeddings of $sl_2$ in a Lie algebra $g$. We give a simple formula for all $W$ transformations, which will enable us to construct the covariant action for general $W$ gravity. It turns out that this covariant action is nothing but a Fourier transform of the WZW action. The same general formula provides a geometrical interpretation of $W$ transformations: they are just homotopy contractions of ordinary gauge transformations. This is used to argue that the moduli space relevant to $W$ gravity is part of the moduli space of $G$-bundles over a Riemann surface.

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