Fusion rules for the logarithmic $N=1$ superconformal minimal models II: including the Ramond sector

TL;DR

This paper extends the fusion rule analysis of logarithmic $N=1$ superconformal minimal models to include the Ramond sector, utilizing advanced fermionic Verlinde formulas and twisted fusion algorithms.

Contribution

It introduces the first detailed construction and analysis of logarithmic structures in the Ramond sector of these models, expanding previous Neveu-Schwarz focused studies.

Findings

Fusion rules including the Ramond sector are derived.

Logarithmic structures in the Ramond sector are constructed and analyzed.

A fermionic Verlinde formula for logarithmic CFTs is applied.

Abstract

The Virasoro logarithmic minimal models were intensively studied by several groups over the last ten years with much attention paid to the fusion rules and the structures of the indecomposable representations that fusion generates. The analogous study of the fusion rules of the $N=1$ superconformal logarithmic minimal models was initiated in arXiv:1504.03155 as a continuum counterpart to the lattice explorations of arXiv:1312.6763. These works restricted fusion considerations to Neveu-Schwarz representations. Here, this is extended to include the Ramond sector. Technical advances that make this possible include a fermionic Verlinde formula applicable to logarithmic conformal field theories and a twisted version of the fusion algorithm of Nahm and Gaberdiel-Kausch. The results include the first construction and detailed analysis of logarithmic structures in the Ramond sector.