Gauge connection between the WZNW system and 2D induced gravity

We introduce a consistent gauge extension of the SL(2, R) WZNW system, defined by a difference of two simple WZNW actions. By integrating out some dynamical variables in the functional integral, we show that the resulting effective theory coincides with the induced gravity in 2D. General solutions of both theories are found and related to each other. 1 Gauge extension of the WZNW system Dynamical structure of two–dimensional (2D) gravity is an important aspect of string theory [1], but it also represents a useful model for the theory of gravitational phenomena in four dimensions. An interesting connection between 2D induced gravity and the SL(2, R) Wess–Zumino–Novikov–Witten (WZNW) model has been discovered both in the light–cone gauge [2] and in the conformal gauge [3, 4]. Here, we present our recent result on the subject [5], showing that the related connection can be established in a covariant way, fully respecting the diffeomorphism invariance of the induced gravity. We formulate a consistent gauge theory of the WZNW system, S(g1, g2) = S(g1)− S(g2) , g1, g2 ∈ SL(2, R) , (1) defined by a difference of two simple WZNW actions, and show, by integrating out some dynamical variables in the functional integral, that the resulting effective theory reduces to the induced gravity in 2D: SG(φ, gμν) = ∫ dξ √ −g [ 2 g∂μφ∂νφ+ 1 2 αφR−M(e − 1)] . (2) General solutions of both theories are constructed, and the related connection between them is discussed [6]. WZNW model. WZNW model in 2D is a field theory described by the action S(g) = S0(v) + nΓ(v) = 1 2 κ ∫