Abstract
We obtain the induced action Γ[h, b] for chiralW 3 gravity in thec→±∞ limit from the induced action of a gaugedSl(3,R) Wess-Zumino-Witten model by imposing constraints on the currents of the latter. In the process we find a closed gauge algebra for the gauge sector ofW 3 gravity in which the currentsT andW become auxiliary fields. An explicit realization ofT andW in terms of the gauge fields is given. In terms of new fieldsr ands, which are a generalization of Polyakov'sf variable for ordinary gravity, the complete induced action Γ[h, b; c→±∞] becomes local.
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Communicated by N. Yu. Reshetikhin
Work supported in part by NSF grant No. PHYS 89-08495
Address after September 1, 1991: Physics Department, U.C. Berkeley, Berkeley, CA 94720, USA
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Ooguri, H., Schoutens, K., Sevrin, A. et al. The induced action ofW 3 gravity. Commun.Math. Phys. 145, 515–539 (1992). https://doi.org/10.1007/BF02099396
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DOI: https://doi.org/10.1007/BF02099396