Exact Renormalization Group and Loop Variables: A Background Independent Approach to String Theory

TL;DR

This paper reviews a background-independent approach to string theory using the Exact Renormalization Group and Loop Variables, deriving gauge invariant equations of motion for string modes in arbitrary backgrounds.

Contribution

It introduces a background-independent method for deriving gauge invariant equations of motion for string modes using Loop Variables and the Exact Renormalization Group.

Findings

Derived interacting equations of motion for string modes.

Demonstrated gauge invariance in arbitrary backgrounds.

Applicable to both open and closed strings.

Abstract

This paper is a self contained review of the Loop Variable approach to string theory. The Exact Renormalization Group is applied to a world sheet theory describing string propagation in a general background involving both massless and massive modes. This gives interacting equations of motion for the modes of the string. Loop variable techniques are used to obtain gauge invariant equations. Since this method is not tied to flat space time or any particular background metric, it is manifestly background independent. The technique can be applied to both open and closed strings. Thus gauge invariant and generally covariant interacting equations of motion can be written for massive higher spin fields in arbitrary backgrounds. Some explicit examples are given.