Related papers: Snowmass White Paper: Moonshine
In earlier work we initiated a program to study relationships between finite groups and arithmetic geometric invariants of modular curves in a systematic way. In the present work we continue this program, with a focus on the two smallest…
This is a Snowmass whitepaper on physical mathematics. It briefly summarizes and highlights some of the key questions drawn from a much more extensive essay, by the same authors, entitled, "A Panorama Of Physical Mathematics 2021."
In 1978, John McKay made an intriguing observation: 196884=196883+1. Monstrous Moonshine is the collection of questions (and a few answers) inspired by this observation. Like moonlight itself, Moonshine is an indirect phenomenon. Just as in…
Over the past few decades, astronomical and cosmological data sets firmly established the existence of physics beyond the Standard Model of particle physics by providing strong evidence for the existence of dark matter, dark energy, and…
This is an informal write up of my talk in Berlin. It gives some background to Goddard's talk (math.QA/9808136) about the moonshine conjectures.
We review the current observational status of string cosmology when confronted with experimental datasets. We begin by defining common observational parameters and discuss how they are determined for a given model. Then we review the…
Symmetry plays a central role in quantum field theory. Recent developments include symmetries that act on defects and other subsystems, and symmetries that are categorical rather than group-like. These generalized notions of symmetry allow…
The aim of this note is to point out an interesting fact related to the elliptic genus of complex algebraic surfaces in the context of Mathieu moonshine. We also discuss the case of 4-folds.
We construct a model of moonshine phenomenon based on the use of N=2 superconformal algebra. We consider an extremal Jacobi form of weight 0 and index 2, and expand it in terms of N=2 massless and massive representations. We find the…
We reiterate that there is significant complementarity between low-energy experiments and high-energy colliders in exploring new physics associated with neutrino properties and their mass generation mechanisms. Signals of the new physics in…
The penumbra of a sunspot is a fascinating phenomenon featuring complex velocity and magnetic fields. It challenges both our understanding of radiative magneto-convection and our means to measure and derive the actual geometry of the…
The aim of these notes is to give recent developments in string theory. In particular, we discuss the string spectrums, compactifications, brane physics and dualities.
The precision cosmological model describing the origin and expansion history of the universe, with observed structure seeded at the inflationary cosmic horizon, demands completion in the ultraviolet and in the infrared. The dynamics of the…
These lectures provide an introduction to supersymmetry phenomenology. They include an overview of the Minimal Supersymmetric Standard Model. The notion of soft breaking is explained, constraints on the standard soft breaking parameters are…
The simplest string theory compactifications to 3D with 16 supercharges -- the heterotic string on $T^7$, and type II strings on $K3 \times T^3$ -- are related by U-duality, and share a moduli space of vacua parametrized by $O(8,24;…
In these notes, based on lectures given in Istanbul, we give an introduction both to Monstrous Moonshine and to the classification of rational conformal field theories, using this as an excuse to explore several related structures and go on…
Currently, string theory represents the only advanced approach to a unification of all interactions, including gravity. In spite of the more than thirty years of its existence it did not make any empirically testable predictions. And it is…
Modern cosmology has created a tight link between particle physics / field theory and a wealth of new observational data on the structure of the Universe. These lecture notes focus on some of the most important aspects concerning the…
Is string theory relevant to the black hole information problem? This is an attempt to clarify some of the issues involved. Presented at Strings '95.
Small fluctuations around homogeneous and isotropic expanding backgrounds are the main object of study in cosmology. Their origin and evolution is sensitive to the physical processes that happen during inflation and in the late Universe. As…