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We review recent developments in understanding quantum/string corrections to BPS black holes and strings in five-dimensional supergravity. These objects are solutions to the effective action obtained from M-theory compactified on a…

These notes are based on lectures given by Michael Green during Part III of the Mathematics Tripos (the Certificate for Advanced Study in Mathematics) in the Spring of 2003. The course provided an introduction to string theory, focussing on…

The roles that spin networks play in gauge theories, quantum gravity and topological quantum field theory are briefly described, with an emphasis on the question of the relationships among them. It is argued that spin networks and their…

This article provides some historical background and then reviews developments in string theory over the last twenty-five years or so. Both perturbative and non-perturbative approaches to string theory are surveyed and their impact on how…

A solution of the vortex type is given in a six-dimensional $SU(2)\times U(1)$ pure gauge theory coupled to Einstein gravity in a compactified background geometry. We construct the solution of an effective abelian Higgs model in terms of…

The well known N=2 string theory describes self-dual gravity, as was shown by Ooguri and Vafa sometime ago. In search of a variant of this theory which would describe self-dual supergravity in 2+2 dimensions, we have constructed two new N=2…

I argue that string creation may have played a role in reheating the universe after inflation. For strings in four dimensions that arise from branes wrapping cycles in the extra dimensions, estimates from effective field theory show that…

String theory developed by demanding consistency with quantum mechanics. In this paper we wish to reverse the reasoning. We pretend open string field theory is a fully consistent definition of the theory - it is at least a self consistent…

Based on well-known properties of semi-classical black holes, we show that weakly-coupled string theory can be viewed as a theory of N = 1/g_s^2 particle species. This statement is a string theoretic realization of the fact that the…

This review talk focusses on some of the interesting developments in the area of superstring compactification that have occurred in the last couple of years. These include the discovery that ``mirror symmetric" pairs of Calabi--Yau spaces,…

In this dissertation we study hidden symmetries within the framework of string theory. There are two kinds of hidden symmetries investigated in this work: the first type is associated with dynamics of quantum fields and the second type is…

These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A…

It has been suggested that reality works like a quantum computer, but such claims are just words if they are not backed up by sound mathematics. In pursuit of the fundamental equations I look to string theory where physicists led by Mike…

String theory is a quantum theory that reproduces the results of General Relativity at long distances but is completely different at short distances. Mathematically, string theory is based on a very new -- and little understood -- framework…

In the present paper we consider quantum theories obtained by quantization of classical theories with first-class constraints assuming that these constraints form a Lie algebra. We show that in this case, one can construct physical…

All the models of elementary particles and their interactions derived from String Theory involve a compact six-dimensional internal space. Its volume and shape should be fixed or stabilized, since otherwise massless scalar fields (moduli)…

Classically, a spin structure on the loop space of a manifold is a lift of the structure group of the looped frame bundle from the loop group to its universal central extension. Heuristically, the loop space of a manifold is spin if and…

We review the current status of the singularity problem in string theory for non-experts. After the problem is discussed from the point of view of supergravity, we discuss classic examples and recent examples of singularity resolution in…

These lectures are devoted to introducing some of the basic features of quantum geometry that have been emerging from compactified string theory over the last couple of years. The developments discussed include new geometric features of…

In superstring theory spin structures are present on both the 2-dimensional worldsheet and 10-dimensional spacetime. We present a new proposal for the B-field in superstring theory and demonstrate its interaction with worldsheet spin…