On-shell Gauge Invariants and Field Strengths in Open Superstring Field Theory

TL;DR

This paper investigates gauge invariant quantities in Berkovits' open superstring field theory, focusing on on-shell invariants related to U(1) field strength and their gauge invariance properties both on- and off-shell.

Contribution

It extends the analysis of gauge invariants from bosonic to superstring field theory, defining and examining quantities related to U(1) field strength and their gauge invariance.

Findings

Field strength from RR coupling is not gauge invariant.

Off-shell field strength from equations of motion is gauge invariant on-shell.

Off-shell gauge invariance under linearized transformations is observed for certain quantities.

Abstract

We study gauge invariant quantities in the open superstring field theory proposed by Berkovits, extending the precedent discussion in bosonic string field theory. Our gauge invariants are ``on-shell''. As its applications, we define quantities which are expected to be related to the U(1) field strength -- a RR coupling and a ``component'' of the string field equation of motion, and consider their naive extensions to off-shell. Order by order calculations show that the field strength extracted from the RR coupling is not gauge invariant, while from the component of the equation of motion we obtain an off-shell field strength which is gauge invariant under full gauge transformation if on-shell, and under linearized gauge transformation even off-shell.