On string cosmology and the RG flow in 2d field theory

TL;DR

This paper explores the relationship between time-dependent string theory solutions and RG flows in 2D field theories, revealing conditions for stable vacua and implications for models with different central charges.

Contribution

It demonstrates that attractive static solutions correspond to minima of |ar c-25| and discusses the forbidden RG flow from c>25 to c<25 models in 2D gravity.

Findings

Attractive solutions are minima of |ar c-25|.

Size of attraction domain relates to vacuum probability.

RG flow from c>25 to c<25 is forbidden.

Abstract

Time-dependent solutions of bosonic string theory resemble renormalisation group trajectories in the space of 2d field theories: they often interpolate between repulsive and attractive static solutions. It is shown that the attractive static solutions are those whose spatial sections are minima of |\bar c-25|, where \bar c is the `c-function'. The size of the domain of attraction of such a solution may be a measure of the probability of the corresponding string vacuum. Our discussion has also an implication for the RG flow in theories coupled to dynamical 2d gravity: the flow from models with c>25 to models with c<25 is forbidden.