Gauge-invariant action for free string field theory with boundary

TL;DR

This work constructs a fully gauge-invariant free string field theory on manifolds with boundary by promoting boundary gauge parameters to dynamical boundary modes, yielding a well-defined variational principle and a BV master-action framework. The core result is the gauge-invariant total action S_tot(Ψ,χ), organized into bulk, bulk–boundary, and boundary pieces, together with a nilpotent BV operator Q_BV and a corresponding master action S_BV that satisfy the classical master equation. The authors provide explicit realizations for massless and first massive open-string levels and the massless closed-string level on a half-space, showing agreement with standard low-energy actions for gravity, Kalb–Ramond, and dilaton, including linear-dilaton backgrounds and boundary fluctuations interpreted as transverse boundary displacements. The formalism demonstrates how boundary dynamics restore gauge invariance in the presence of a boundary and offers a path toward understanding string interactions with boundaries, including extensions to linear-dilaton backgrounds and potential BV–BFV formulations for curved boundaries.

Abstract

We construct fully gauge-invariant kinetic terms for open and closed string field theories on a target space with boundary. This is realized by promoting the gauge parameters at the boundary to extra dynamical modes describing boundary degrees of freedom. Having a gauge-invariant classical action, we also construct the corresponding BV master action and show that the master equation is obeyed thanks to a peculiar nilpotent structure of the BV kinetic operator. From this general construction we explicitly derive free actions for massless and massive modes of open and closed strings propagating on a target with a boundary, including linear-dilaton backgrounds.