Exact marginality in open string field theory: a general framework

TL;DR

This paper develops a general framework for constructing exact solutions in open bosonic string field theory for any exactly marginal boundary conformal field theory deformation, using renormalized operators and a modified star product.

Contribution

It introduces a comprehensive method for analytic solutions in string field theory for various marginal deformations, including those involving gauge fields and scalar fields on D-branes.

Findings

Explicit renormalized operator products for specific deformations

Construction of solutions using integrated vertex operators

Introduction of a modified star product for deformed backgrounds

Abstract

We construct analytic solutions of open bosonic string field theory for any exactly marginal deformation in any boundary conformal field theory when properly renormalized operator products of the marginal operator are given. We explicitly provide such renormalized operator products for a class of marginal deformations which include the deformations of flat D-branes in flat backgrounds by constant massless modes of the gauge field and of the scalar fields on the D-branes, the cosine potential for a space-like coordinate, and the hyperbolic cosine potential for the time-like coordinate. In our construction we use integrated vertex operators, which are closely related to finite deformations in boundary conformal field theory, while previous analytic solutions were based on unintegrated vertex operators. We also introduce a modified star product to formulate string field theory around the deformed background.