Classical Open-String Field Theory ; $A_{\infty}$-Algebra, Renormalization Group and Boundary States

TL;DR

This paper explores classical bosonic open-string field theory through the lens of the Wilson renormalization group, connecting it with $A_{ abla}$-algebra deformation theory and boundary states, using the BV formalism.

Contribution

It introduces a renormalization group framework for classical open-string field theory and links it with $A_{ abla}$-algebra deformation and boundary state interpretations.

Findings

The theory is deeply related to $A_{ abla}$-algebra deformation.

A renormalization group equation for the theory is formulated.

Boundary states and closed-string BRST charge are integral to the framework.

Abstract

We investigate classical bosonic open-string field theory from the perspective of the Wilson renormalization group of world-sheet theory. The microscopic action is identified with Witten's covariant cubic action and the short-distance cut-off scale is introduced by length of open-string strip which appears in the Schwinger representation of open-string propagator. {\it Classical open-string field theory} in the title means open-string field theory governed by a classical part of the low energy action. It is obtained by integrating out suitable tree interactions of open-strings and is of non-polynomial type. We study this theory by using the BV formalism. It turns out to be deeply related with deformation theory of $A_{\infty}$-algebra. We introduce renormalization group equation of this theory and discuss it from several aspects. It is also discussed that this theory is interpreted as a boundary open-string field theory. Closed-string BRST charge and boundary states of closed-string field theory in the presence of open-string field play important roles.