# Albion Lawrence : Worldsheet RG and target space time evolution

A useful tool to study tachyon condensation in string theory is the renormalization group flow of the associated relevant perturbation of a conformal field theory. One assumes that the worldsheet RG flow reflects the actual time evolution of the target space. The relationship is not completely direct: for example, the RG equations are first order differential equations, while the target space equations of motion are at least second order in time. To put the correspondence on firmer footing we discuss the coupling of non-conformal 2d field theories with $n\geq 25$ scalar fields to 2d gravity, following previous discussions of Polyakov and of Schmidhuber and Tseytlin. The conformal mode of the metric becomes a timelike target space direction with a Liouville action, so that the Liouville dressing of an operator is related to its scaling properties. We will give a conjecture for the equations of motion for the worldsheet couplings, which reduces to the standard 2d RG equations in the limit that the Liouville mode becomes semiclassical, and describe our current attempts to prove this conjecture.

**Category**: String Theory**Duration**: 01:03:09**Date**: February 24, 2005 at 2:45 PM**Views**: 33-
**Tags:**seminar, String Theory Seminar

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