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

Sudhakar Panda·Shibaji Roy
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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.

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Sudhakar Panda, Shibaji Roy. 1995-07-09. BRST Cohomology Ring in ${\hat c_M}<1$ NSR String Theory. https://doi.org/10.1016/0370-2693(95)01019-m

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