Open string stub as an auxiliary string field

TL;DR

This paper reformulates open string field theory with generalized stubs as a cubic theory using an auxiliary field, analyzing gauge symmetries, algebraic structure, and implications for closed string interactions.

Contribution

It introduces an auxiliary string field to incorporate stubs into open string field theory, providing a new perspective on deformations and their algebraic properties.

Findings

Recovering conventional cubic theory by integrating out fields

Describing stub deformations via homotopy transfer

Discussing stub vertex regions as models for closed string interactions

Abstract

Witten's open string field theory with a generalized version of stubs is reformulated as a cubic string field theory using an auxiliary string field. The gauge symmetries and equations of motion as well as the associative algebra of the resulting theory are investigated. Integrating out either the original or auxiliary field is shown to recover the conventional cubic theory. Our analysis demonstrates that deformations due to the stubs can be described as a homotopy transfer purely in the context of strong deformation retract. We also discuss to what extent the vertex regions resulting from stubs provide a model for the elementary interactions of closed string field theory.