BRST Cohomology Ring in ${\hat{c}}_M<1$ NSR String Theory

Abstract

The full cohomology ring of the Lian-Zuckerman type operators (states) in ${\hat{c}}_M<1$ Neveu-Schwarz-Ramond (NSR) string theory is argued to be generated by three elements $x$, $y$ and $w$ in analogy with the corresponding results in the bosonic case. The ground ring generators $x$ and $y$ are non-invertible and belong to the Ramond sector whereas the higher ghost number operators are generated by an invertible element $w$ with ghost number one less than that of the ground ring generators and belongs to either Neveu-Schwarz (NS) or Ramond (R) sector depending on whether we consider (even, even) or (odd, odd) series coupled to $2d$ supergravity. We explicitly construct these operators (states) and illustrate our result with an example of pure Liouville supergravity.

16 pages, Latex, no figures

References in corpus (6)

• Algebraic Structures and Differential Geometry in 2D String Theory
• Interaction of Discrete States in Two-Dimensional String Theory
• Ground Rings and Their Modules in 2D Gravity with $c\le 1$ Matter
• Brst Cohomology and Physical States in 2D Supergravity Coupled to $\hat{c}\le 1$ Matter
• Ground ring for the 2D NSR string
• On the Symmetry Algebra of the Discrete States in $d<2$ Closed String Theory

Cited by in corpus (2)

• Branes, Rings and Matrix Models in Minimal (Super)string Theory
• Heterotic Strings in Two Dimensions and New Stringy Phase Transitions