Snowmass White Paper: Moonshine

TL;DR

This paper reviews the Moonshine phenomena, highlighting its connections to physics, group theory, number theory, and conformal field theories, and discusses recent developments and open questions in the field.

Contribution

It provides a comprehensive overview of Moonshine, emphasizing its interdisciplinary connections and recent advances in understanding its role in physics and mathematics.

Findings

Moonshine links group theory with number theory and conformal field theories.

Recent developments connect Moonshine to string theory and enumerative geometry.

Open questions remain about the full scope and implications of Moonshine phenomena.

Abstract

We present a brief overview of Moonshine with an emphasis on connections to physics. Moonshine collectively refers to a set of phenomena connecting group theory, analytic number theory, and vertex operator algebras or conformal field theories. Modern incarnations of Moonshine arise in various BPS observables in string theory and, via dualities, invariants in enumerative geometry. We survey old and new developments, and highlight some of the many open questions that remain.