Abstract

We find the solution of the Weyl invariance conditions for a D = 2 σ model with an isometry in the three-loop approximation. The resulting metric-dilaton background is compared with the α' expansion of the exact “black hole” background suggested by Dijkgraaf, Verlinde and Verlinde [Princeton preprint PUPT 1252/91] to correspond to the SL(2, R) U(1) gauged WZW conformal theory.

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