Role of Short Distance Behavior in Off-Shell Open-String Field Theory

TL;DR

This paper investigates a background independent open string field theory with quadratic boundary interactions, demonstrating how renormalization renders the theory finite and cut-off independent despite some unrenormalizable couplings.

Contribution

It introduces a short-distance cut-off and shows how renormalization manages boundary couplings to achieve a finite, background independent string field theory.

Findings

Renormalization makes the partition function finite and cut-off independent.

The string field action depends on the leading unrenormalizable coupling.

A finite number of local boundary couplings can describe the theory.

Abstract

A recent proposal for a background independent open string field theory is studied in detail for a class of backgrounds that correspond to general quadratic boundary interactions on the world-sheet. A short-distance cut-off is introduced to formulate the theory with a finite number of local and potentially unrenormalizable boundary couplings. It is shown that renormalization of the boundary couplings makes both the world-sheet partition function and the string field action finite and cut-off independent, although the resulting string field action has an unpalatable dependence on the leading unrenormalizable coupling.