Boundary Modes in String Field Theory

TL;DR

This paper constructs boundary terms in bosonic string field theory actions to ensure well-defined variational principles, revealing connections to general relativity and higher-spin theories, and suggesting extensions to full tensile string theory.

Contribution

It introduces a method to add boundary contributions for gauge invariance in string field theory, including explicit constructions for massless levels and the tensionless limit.

Findings

Reproduces linearized general relativity with Gibbons-Hawking-York term

Provides gauge-invariant actions for massless higher-spin theories

Suggests possible extension to full tensile string field theory

Abstract

We discuss the construction of boundary contributions to free string field theory actions in the context of the bosonic string. We show that it is generally possible to obtain a well-defined variational principle by adding a simple boundary term (which only depends on the value of the bulk fields at the boundary) to the original bulk action. However, it is in general not possible to do this in a gauge-invariant way unless suitable boundary degrees of freedom are added. We explicitly construct such boundary contributions for the massless level of both the open and the closed SFT, as well as for the tensionless limit of the full string field theory. Our results reproduce linearized general relativity with the Gibbons-Hawking-York term and provide similar gauge-invariant actions for the infinite tower of massless higher-spin gauge theories for all Regge trajectories. By writing down a gauge-invariant action for the first massive level of the open string, we provide evidence that an analogous construction should be possible for the full tensile string field theory.