Loop Variables and Gauge Invariant Exact Renormalization Group Equations for (Open) String Theory

TL;DR

This paper develops a gauge-invariant exact renormalization group equation for open string theory using loop variable techniques, providing a background-independent, quadratic string field theory proposal that includes interactions expressed via gauge-invariant field strengths.

Contribution

It introduces a novel gauge-invariant ERG equation for open strings, explicitly worked out up to level 3, with a new approach to interactions via gauge-invariant field strengths.

Findings

Equation is quadratic in fields and background independent.

Gauge transformations remain unmodified by interactions up to level 3.

Interactions are expressed in terms of gauge-invariant field strengths.

Abstract

An exact renormalization group equation is written down for the world sheet theory describing the bosonic open string in general backgrounds. Loop variable techniques are used to make the equation gauge invariant. This is worked out explicitly up to level 3. The equation is quadratic in the fields and can be viewed as a proposal for a string field theory equation. As in the earlier loop variable approach, the theory has one extra space dimension and mass is obtained by dimensional reduction. Being based on the sigma model RG, it is background independent. It is intriguing that in contrast to BRST string field theory, the gauge transformations are not modified by the interactions up to the level calculated. The interactions can be written in terms of gauge invariant field strengths for the massive higher spin fields and the non zero mass is essential for this. This is reminiscent of Abelian Born-Infeld action (along with derivative corrections) for the massless vector field, which is also written in terms of the field strength.