NSR Open Super-string in the proper-time gauge I: Free Field Theory

TL;DR

This paper derives the free-field actions for open super-strings in the NS and R sectors using the proper-time gauge, providing a covariant formulation based on the Polyakov path integral.

Contribution

It presents a covariant derivation of open super-string free-field actions in the proper-time gauge, contrasting with traditional light-cone gauge approaches.

Findings

Derived free-string actions for NS and R sectors.

Established proper-time as a key parameter in the covariant formulation.

Provided a framework for covariant super-string field theory.

Abstract

We study the Neveu-Schwarz-Ramond (NSR) open super-string theory in the proper-time gauge. The string field action is obtained by evaluating the Polyakov string path integral. In this study, we focus on the open-string free-field action, which corresponds to the string path integral on a strip. Depending on the periodicity of the fermion fields, the open super-string has two sectors: The Neveu-Schwarz (NS) and Ramond (R) sectors. We can impose the gauge conditions to fix the (super-) reparametrization invariance on the two-dimensional metric and its super-partner on the string world sheet to secure the covariance, in contrast to the light-cone gauge condition. Accordingly, the proper-time emerges in the NS sector and both proper-time and its super-partner appear in the R-sector. Integration leads to free-string field actions in both sectors.