The Boundary State Formalism and Conformal Invariance in Off-shell String Theory

TL;DR

This paper extends the boundary state formalism in bosonic string theory to accurately compute overlaps with both on-shell and off-shell states, aligning with sigma model results and ensuring consistency with non-conformal boundary interactions.

Contribution

It introduces a generalized boundary state formalism that reproduces sigma model calculations and handles off-shell states in string theory.

Findings

Exact reproduction of sigma model overlaps

Automatic satisfaction of integrated vertex operator conditions

Compatibility with non-conformal boundary interactions

Abstract

We present a generalization of the boundary state formalism for the bosonic string that allows us to calculate the overlap of the boundary state with arbitrary closed string states. We show that this generalization exactly reproduces world-sheet sigma model calculations, thus giving the correct overlap with both on- and off-shell string states, and that this new boundary state automatically satisfies the requirement for integrated vertex operators in the case of non-conformally invariant boundary interactions.