String vacuum backgrounds with covariantly constant null Killing vector and 2d quantum gravity

Abstract

We consider a $2d$ sigma model with a $2+N$ - dimensional Minkowski signature target space metric having a covariantly constant null Killing vector. We study solutions of the conformal invariance conditions in $2+N$ dimensions and find that generic solutions can be represented in terms of the RG flow in $N$ - dimensional ``transverse space'' theory. The resulting conformal invariant sigma model is interpreted as a quantum action of the $2d$ scalar (``dilaton") quantum gravity model coupled to a (non-conformal) `transverse' sigma model. The conformal factor of the $2d$ metric is identified with a light cone coordinate of the $2+N$ - dimensional sigma model. We also discuss the case when the transverse theory is conformal (with or without the antisymmetric tensor background) and reproduce in a systematic way the solutions with flat transverse space known before.

26 p., revised (a discussion of tachyon coupling is added at the end of section 4), DAMTP-92-49

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• Scalar-Tensor Quantum Gravity in Two Dimensions
• A class of finite two - dimensional sigma models and string vacua
• Classical and Quantum Considerations of Two-dimensional Gravity
• Two-loop finiteness of D=2 supergravity

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