Renormalization group flow of reduced string actions

Abstract

It has been argued that certain reduced actions play a role in AdS/CFT when comparing fast moving strings to long single trace operators in gauge theories. Such actions arise in two ways: as a limit of the string action and as a description of long single trace field theory operators. They are non-relativistic sigma models with the target space usually being a Kahler manifold. They are non-renormalizable and need a cut-off in the wave-length. If the total spin (or charge) contained in a minimal wavelength is large compared to one, the system behaves approximately classically and an expansion in loops is meaningful. In this paper we apply the renormalization group procedure to such actions and find, at one-loop, that the Kahler potential flows in the infrared to a Kahler-Einstein one.Therefore, in this context, the anomalous dimensions of long operators are determined by a fixed point. This suggests that certain features of the large N-limit might be independent of the detailed properties of a gauge theory.