Fusion rules for the logarithmic $N=1$ superconformal minimal models I: the Neveu-Schwarz sector

TL;DR

This paper investigates the fusion rules of the Neveu-Schwarz sector in logarithmic N=1 superconformal minimal models, advancing understanding of their algebraic structure relevant to non-local observables in critical systems.

Contribution

It provides the first detailed analysis of fusion rules for the N=1 supersymmetric logarithmic minimal models in the Neveu-Schwarz sector, building on prior work on non-supersymmetric cases.

Findings

Derived explicit fusion rules for the Neveu-Schwarz sector

Connected fusion rules to lattice model conjectures

Set the stage for future analysis of Ramond sector

Abstract

It is now well known that non-local observables in critical statistical lattice models, polymers and percolation for example, may be modelled in the continuum scaling limit by logarithmic conformal field theories. Fusion rules for such theories, sometimes referred to as logarithmic minimal models, have been intensively studied over the last ten years in order to explore the representation-theoretic structures relevant to non-local observables. Motivated by recent lattice conjectures, this work studies the fusion rules of the $N=1$ supersymmetric analogues of these logarithmic minimal models in the Neveu-Schwarz sector. Fusion rules involving Ramond representations will be addressed in a sequel.