Gauge Invariant Exact Renormalization Group and Perfect Actions in the Open Bosonic String Theory

TL;DR

This paper develops a gauge-invariant exact renormalization group approach for open bosonic string theory, enabling the derivation of off-shell equations of motion while maintaining a finite world sheet cutoff, akin to perfect actions in lattice gauge theory.

Contribution

It introduces a gauge-invariant, scale-invariant renormalization group framework for open string backgrounds that remains valid off-shell with a finite cutoff, using loop variable techniques.

Findings

Derived gauge-invariant equations of motion for open string fields.

Maintained scale invariance with a finite world sheet cutoff.

Connected the approach to the concept of perfect actions in lattice gauge theory.

Abstract

The exact renormalization group is applied to the world sheet theory describing bosonic open string backgrounds to obtain the equations of motion for the fields of the open string. Using loop variable techniques the equations can be constructed to be gauge invariant. Furthermore they are valid off the (free) mass shell. This requires keeping a finite cutoff. Thus we have the interesting situation of a scale invariant world sheet theory with a finite world sheet cutoff. This is possible because there are an infinite number of operators whose coefficients can be tuned. This is in the same sense that "perfect actions" or "improved actions" have been proposed in lattice gauge theory to reproduce the continuum results even while keeping a finite lattice spacing.