Light-cone Gauge NSR Strings in Noncritical Dimensions II -- Ramond Sector

TL;DR

This paper develops a free-variable formulation of the Ramond sector in noncritical light-cone gauge superstring theory, enabling BRST invariant amplitude calculations in a conformal gauge framework.

Contribution

It introduces a free-variable representation of the X^{} CFT combined with ghost systems, facilitating explicit construction of spin fields and vertex operators for the Ramond sector.

Findings

Constructed BRST invariant vertex operators for the Ramond sector.

Expressed tree amplitudes in a BRST invariant form for noncritical superstrings.

Provided a method to compute amplitudes with external Ramond and Neveu-Schwarz states.

Abstract

Light-cone gauge superstring theory in noncritical dimensions corresponds to a worldsheet theory with nonstandard longitudinal part in the conformal gauge. The longitudinal part of the worldsheet theory is a superconformal field theory called X^{\pm} CFT. We show that the X^{\pm} CFT combined with the super-reparametrization ghost system can be described by free variables. It is possible to express the correlation functions in terms of these free variables. Bosonizing the free variables, we construct the spin fields and BRST invariant vertex operators for the Ramond sector in the conformal gauge formulation. By using these vertex operators, we can rewrite the tree amplitudes of the noncritical light-cone gauge string field theory, with external lines in the (R,R) sector as well as those in the (NS,NS) sector, in a BRST invariant way.