BRST cohomology ring in ĉM < 1 NSR string theory

The full cohomology ring of the Lian-Zuckerman type operators (states) in ĉM < 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 that belongs to either the 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.