A boundary term for open string field theory

TL;DR

This paper derives a boundary term for open string field theory in spacetimes with boundaries, ensuring a well-defined variational principle, and discusses boundary contributions from the cubic vertex.

Contribution

It introduces a Gibbons-Hawking-type boundary term for open string field theory and analyzes boundary effects on the cubic interaction vertex.

Findings

Derived a boundary term for the kinetic part of the action

Confirmed the boundary term using a path integral approach

Discussed challenges in applying boundary conditions to the cubic vertex

Abstract

We consider Witten's open string field theory in the presence of a non-trivial boundary of spacetime. For the kinetic term, we derive a Gibbons-Hawking-type contribution that has to be added to the action to guarantee a well-defined variational principle. The derivation is done first in a heuristic way and then confirmed by a path integral based approach using the CFT operator formalism. In the last section we discuss the boundary contributions coming from the cubic vertex, although it is problematic to apply consistent boundary conditions on the string field due to the non-locality of the vertex.