Tadpoles and Closed String Backgrounds in Open String Field Theory

TL;DR

This paper analyzes the quantum structure of open bosonic string field theory, revealing divergences and BRST invariance issues in one-loop tadpole calculations, and discusses potential remedies and implications for supersymmetric theories.

Contribution

It provides a detailed one-loop analysis of the open string tadpole, identifying divergences and proposing methods to handle them, with implications for the consistency of quantum open string field theory.

Findings

Divergences and BRST invariance breakdown in tadpole diagrams

Analytic continuation of the closed string tachyon can render the tadpole finite for certain Dp-branes

Higher-loop divergences threaten the consistency of bosonic open string field theory

Abstract

We investigate the quantum structure of Witten's cubic open bosonic string field theory by computing the one-loop contribution to the open string tadpole using both oscillator and conformal field theory methods. We find divergences and a breakdown of BRST invariance in the tadpole diagram arising from tachyonic and massless closed string states, and we discuss ways of treating these problems. For a Dp-brane with sufficiently many transverse dimensions, the tadpole can be rendered finite by analytically continuing the closed string tachyon by hand; this diagram then naturally incorporates the (linearized) shift of the closed string background due to the presence of the brane. We observe that divergences at higher loops will doom any straightforward attempt at analyzing general quantum effects in bosonic open string field theory on a Dp-brane of any dimension, but our analysis does not uncover any potential obstacles to the existence of a sensible quantum open string field theory in the supersymmetric case.