Related papers: TASI Lectures on Moonshine
A brief, example-oriented introduction is given to special holonomy and its uses in string theory and M-theory. We discuss A_k singularities and their resolution; the construction of a K3 surface by resolving T^4/Z_2; holomorphic cycles,…
String theory can accommodate black holes with the black hole parameters related to string moduli. It is a well known but remarkable feature that the near horizon geometry of a large class of black holes arising from string theory contains…
The purpose of this short review is to present progresses in string theory in the recent past. There have been very important developments in our understanding of string dynamics, especially in the nonperturbative aspects. In this context,…
In this work we provide a self-contained and modern introduction to some of the tools, obstacles and open questions arising in string compactifications. Techniques and current progress are illustrated in the context of smooth heterotic…
Observational evidence and theoretical motivation for dark matter are presented and connections to the CMB and BBN are made. Problems for baryonic and neutrino dark matter are summarized. Emphasis is placed on the prospects for…
Phys and Math are two colleagues at the University of Sa{\c c}enbon (Crefan Kingdom), dialoguing about the remarkable efficiency of mathematics for physics. They talk about the notches on the Ishango bone, the various uses of psi in maths…
This is a short summary of my lectures given at the Fourth Mexican School on Gravitation and Mathematical Physics. These lectures gave a brief introduction to black holes in string theory, in which I primarily focussed on describing some of…
These notes stem from lectures given by the first author (JM) at the 2008 "Moonshine Conference in Kashiwa" and contain a number of new perspectives and observations on Monstrous Moonshine. Because many new points have not appeared anywhere…
We show interesting relations between extremal partition functions of a family of conformal field theories and dimensions of the irreducible representations of the Fischer-Griess Monster sporadic group. We argue that these relations can be…
We present five open problems in the theory of vertex rings. They cover a variety of different areas of research where vertex rings have been, or are threatening to be, relevant. They have also been chosen because I personally find them…
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…
Recent progress on the complete set of solutions of two dimensional classical string theory in any curved spacetime is reviewed. When the curvature is smooth the string solutions are deformed folded string solutions as compared to flat…
Supersymmetric extreme dyonic black holes of toroidally compactified heterotic or type II string theory can be viewed as lower-dimensional images of solitonic strings wound around a compact dimension. We consider conformal sigma models…
We construct super vertex operator algebras which lead to modules for moonshine relations connecting the four smaller sporadic simple Mathieu groups with distinguished mock modular forms. Starting with an orbifold of a free fermion theory,…
This is an introduction to some recent developments in string theory and M theory. We try to concentrate on the main physical aspects, and often leave more technical details to the original literature.
These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.
We give an introductory review of topological strings and their application to various aspects of superstrings and supersymmetric gauge theories. This review includes developing the necessary mathematical background for topological strings,…
These are notes from my lectures at TASI 2015. The goal is to provide context for the study of strongly-correlated quantum many-body systems using quantum field theory, and possibly string theory.
Black holes are a continuing source of mystery. Although their classical properties have been understood since the 1970's, their quantum properties raise some of the deepest questions in theoretical physics. Some of these questions have…
String Theory is a hot topic of physics and mathematics. For the former, it stands as a huge sandbox where the formulation of difficult problems can be simplified and their hard computations carried out. For the latter, it stands as a…