RG flow in 2d field theory coupled to gravity

Abstract

The renormalization group flow in two--dimensional field theories is modified if they are coupled to gravity. Beta function coefficients are changed, the $c$--theorem is no longer strictly valid, and flows from fixed points with central charge $c>25$ to fixed points with $c<25$ are forbidden. This is discussed in general and at two examples, the Kosterlitz--Thouless phase transition and the Wess--Zumino--Witten model. A possible application to string cosmology is pointed out.