One-Loop Riemann Surfaces in Schnabl Gauge

TL;DR

This paper demonstrates that one-loop string diagrams in Schnabl gauge produce the relevant closed string moduli through the use of slanted wedges, simplifying the calculation of moduli compared to other gauges.

Contribution

It reveals that closed string moduli are generated in Schnabl gauge via slanted wedges, providing a simplified method for calculating moduli in one-loop diagrams.

Findings

Closed string moduli are always produced in one-loop diagrams in Schnabl gauge.

Conformal maps in Schnabl gauge are greatly simplified, making moduli functions of Schwinger parameters.

The approach offers a simplification not present in Siegel or light-cone gauges.

Abstract

Due to a peculiar behavior at the open string midpoint, loop diagrams in Schnabl gauge were expected to fail to produce the relevant closed string moduli. We find that closed string moduli are generated because the Riemann surfaces are built with slanted wedges: semi-infinite strips whose edges have parameterizations related by scaling. We examine in detail one-loop string diagrams and find that the closed string modulus is always produced. Moreover, the conformal maps simplify so greatly that both closed and open moduli become simple calculable functions of the Schwinger parameters, a simplification that occurs neither in Siegel gauge nor in light-cone gauge.