Linear b-Gauges for Open String Fields

TL;DR

This paper investigates linear b-gauges in open string field theory, deriving propagators, analyzing their properties, and constructing a family of gauges that interpolate between known gauges, ensuring correct amplitude reproduction.

Contribution

It introduces a class of regular linear b-gauges with rigorous properties and constructs interpolating gauges between Siegel and Schnabl gauges.

Findings

Identified conditions for propagator regularization

Proved properties ensuring correct on-shell amplitudes

Constructed interpolating gauges between known gauge choices

Abstract

Motivated by Schnabl's gauge choice, we explore open string perturbation theory in gauges where a linear combination of antighost oscillators annihilates the string field. We find that in these linear b-gauges different gauge conditions are needed at different ghost numbers. We derive the full propagator and prove the formal properties which guarantee that the Feynman diagrams reproduce the correct on-shell amplitudes. We find that these properties can fail due to the need to regularize the propagator, and identify a large class of linear b-gauges for which they hold rigorously. In these gauges the propagator has a non-anomalous Schwinger representation and builds Riemann surfaces by adding strip-like domains. Projector-based gauges, like Schnabl's, are not in this class of gauges but we construct a family of regular linear b-gauges which interpolate between Siegel gauge and Schnabl gauge.