Beauty And The Beast Part 2: Apprehending The Missing Supercurrent

TL;DR

This paper constructs explicit superconformal currents within a spin lift of the Moonshine conformal field theory, utilizing error correcting codes to fill a gap in the understanding of its superconformal symmetry.

Contribution

It provides the first explicit construction of superconformal currents in a spin lift of the Moonshine CFT, advancing the understanding of its superconformal symmetry.

Findings

Constructed several superconformal currents using error correcting codes.

Filled the gap in explicit superconformal current construction for the Moonshine CFT.

Enhanced the understanding of superconformal symmetry in the Moonshine module.

Abstract

The Moonshine module is a $c=24$ conformal field theory (CFT) whose automorphism group is the Monster group. It was argued by Dixon, Ginsparg, and Harvey in \cite{Dixon:1988qd} that there exists a spin lift of the Moonshine CFT with superconformal symmetry. Reference \cite{Dixon:1988qd} did not provide an explicit construction of a superconformal current. The present paper fills that gap. In fact, we will construct several superconformal currents in a spin lift of the Moonshine CFT using techniques developed in \cite{Harvey:2020jvu}. In particular, our construction relies on error correcting codes.