A Borcherds-Kac-Moody superalgebra with Conway symmetry

TL;DR

This paper constructs a new Borcherds-Kac-Moody superalgebra with Conway group symmetry, linking string theory, moonshine phenomena, and genus zero properties, and explores its implications for BPS states in string theory.

Contribution

It introduces a novel BKM superalgebra with Conway symmetry generated from superstring states, connecting moonshine and string theory.

Findings

Constructed a BKM superalgebra with Co$_0$ symmetry.

Derived denominator identities for Conway module partition functions.

Proposed a physical interpretation of Conway moonshine in string theory.

Abstract

We construct a Borcherds Kac-Moody (BKM) superalgebra on which the Conway group Co$_0$ acts faithfully. We show that the BKM algebra is generated by the BRST-closed states in a chiral superstring theory. We use this construction to produce denominator identities for the chiral partition functions of the Conway module $V^{s\natural}$, a supersymmetric $c=12$ chiral conformal field theory whose (twisted) partition functions enjoy moonshine properties and which has automorphism group isomorphic to Co$_0$. In particular, these functions satisfy a genus zero property analogous to that of monstrous moonshine. Finally, we suggest how one may promote the denominators to spacetime BPS indices in type II string theory, which might thus furnish a physical explanation of the genus zero property of Conway moonshine.