Exact effective action and spacetime geometry in gauged WZW models.

Abstract

We present an effective quantum action for the gauged WZW model ${\mathit{G}}_{\mathrm{\ensuremath{-}}\mathit{k}}$/${\mathit{H}}_{\mathrm{\ensuremath{-}}\mathit{k}}$. It is conjectured that it is valid to all orders of the central extension (-k) on the basis that it reproduces the exact spacetime geometry of the zero modes that was previously derived in the algebraic Hamiltonian formalism. In addition to the metric and dilaton, the new results that follow from this approach include the exact axion field and the solution of the geodesics in the exact geometry. It is found that the axion field is generally nonzero at higher orders of 1/k even if it vanishes at large k. We work out the details in two specific coset models: one non-Abelian, i.e., SO(2,2)/SO(2,1), and one Abelian, i.e., SL(2,openR)\ensuremath{\bigotimes}SO(1,1${)}^{\mathit{d}\mathrm{\ensuremath{-}}2}$/SO(1,1). The simplest case SL(2,openR)/openR corresponds to a limit.