Related papers: TASI Lectures on Moonshine
We consider thorny spheres, that is 2-dimensional compact surfaces which are everywhere locally isometric to a round sphere $S^2$ except for a finite number of isolated points where they have conical singularities. We use thorny spheres to…
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.
We show that the recently discovered Mathieu moonshine plays a role for certain four dimensional theories with $\mathcal{N}=1$ supersymmetry. These theories are obtained from the $E_8 \times E_8$ heterotic string theory by compactifying on…
These lectures aim to provide a global picture of the spaces of consistent quantum supergravity theories and string vacua in higher dimensions. The lectures focus on theories in the even dimensions 10, 8, and 6. Supersymmetry, along with…
This is a historical talk about the recent confluence of two lines of research in equivariant elliptic cohomology, one concerned with connected Lie groups, the other with the finite case. These themes come together in (what seems to me…
We review recent progress in our understanding of the physics of black holes. In particular, we discuss the ideas from string theory that explain the entropy of black holes from a counting of microstates of the hole, and the related…
String theory avoids the ultraviolet infinities that arise in trying to quantize gravity. It is also more predictive than conventional quantum field theory, one aspect of this being the way that it contributed to the emergence of the…
A very brief review is given of some of the developments leading to our current understanding of black holes in string theory. This is followed by a discussion of two possible misconceptions in this subject - one involving the stability of…
An arithmetic framework to string compactification is described. The approach is exemplified by formulating a strategy that allows to construct geometric compactifications from exactly solvable theories at $c=3$. It is shown that the…
The Conway--Norton conjectures unexpectedly related the Monster with certain special modular functions (Hauptmoduls). Their proof by Borcherds et al was remarkable for demonstrating the rich mathematics implicit there. Unfortunately…
In these lecture notes, we review some recent developments on the relation between the macroscopic entropy of four-dimensional BPS black holes and the microscopic counting of states, beyond the thermodynamical, large charge limit. After a…
In this set of lectures I review recent developments in string theory emphasizing their non-perturbative aspects and their recently discovered duality symmetries. The goal of the lectures is to make the recent exciting developments in…
We show that in string theory, due to non-perturbative effects, there are cases in which two states that semi-classically are completely different, are in fact the same. One state cannot be excited without exciting the other; they are two…
The Distance Conjecture states that an infinite tower of modes becomes exponentially light when approaching an infinite distance point in field space. We argue that the inherent path-dependence of this statement can be addressed when…
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.
Supersymmetry-breaking is a key ingredient for string theory models to be phenomenologically viable. We review the strong analogy in the physics and the methods used for describing non-supersymmetric flux vacua and non-supersymmetric black…
F-theory is perhaps the most general currently available approach to study non-perturbative string compactifications in their geometric, large radius regime. It opens up a wide and ever-growing range of applications and connections to…
This thesis investigates two main topics concerning black holes in extensions of general relativity inspired by string theory. First, the structure of the equations of motion underlying black hole solutions is considered, in theories of…
String theory and supersymmetry are theoretical ideas that go beyond the standard model of particle physics and show promise for unifying all forces. After a brief introduction to supersymmetry, we discuss the prospects for its experimental…
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…