We give a simple proof of the known S-duality of Heterotic String theory compactified on a T6. Using this S-duality we calculate the tensions for a class of BPS 5-branes in Heterotic String theory on a S1. One of these, the Kaluza-Klein monopole, becomes tensionless when the radius of the S1 is equal to the string length. We study the question of stability of the Heterotic NS5-brane with a tran...

The conjectured equivalence of the heterotic string to a K3 compactified type IIA superstring is combined with the conjectured equivalence of the latter to a compactified 11-dimensional supermembrane to derive a string membrane duality in seven dimensions; the membrane is a soliton of the string theory and vice versa. A prediction of this duality is that the heterotic string is a K3 compactific...

In this lecture I summarize recent developments on strings propagating in curved spacetime. Exact conformal field theories that describe gravitational backgrounds such as black holes and more intricate gravitational singularities have been discovered and investigated at the classical and quantum level. These models are described by gauged Wess-Zumino-Witten models, or equivalently current algeb...

We search for realistic supersymmetric standard-like models from SO(32) heterotic string theory on factorizable tori with multiple magnetic fluxes. Three chiral ganerations of quarks and leptons are derived from the adjoint and vector representations of SO(12) gauge groups embedded in SO(32) adjoint representation. Massless spectra of our models also include Higgs fields, which have desired Yuk...

We study heterotic/type I duality in d = 8, 9 uncompactified dimensions. We consider the special (“BPS saturated”) F4 and R4 terms in the effective one-loop heterotic action, which are expected to be non-perturbatively exact. Under the standard duality map these translate to tree-level, perturbative and non-perturbative contributions on the type I side. We check agreement with the one-loop open...

In this paper we consider compactifications of type I strings on Abelian orbifolds. We discuss the tadpole cancellation conditions for the general case with D9-branes only. Such compactifications have (perturbative) heterotic duals which are also realized as orbifolds (with non-standard embedding of the gauge connection). The latter have extra twisted states that become massive once orbifold si...

Anomalous U(1) gauge symmetries can appear both in heterotic and type I string theories. In the heterotic case we find a single anomalous U(1), while in open string theories several such symmetries can appear. Nonetheless, there is a conjectured duality symmetry that might connect these two theories. We review the properties of anomalous gauge symmetries in various string theories as well as th...

We examine the recently proposed relations between black hole entropy and the topological string in the context of type II/heterotic string dual models. We consider the degeneracies of perturbative heterotic BPS states. In several examples with N = 4 and N = 2 supersymmetry, we show that the macroscopic degeneracy of small black holes agrees to all orders with the microscopic degeneracy, but mi...

These lectures begin by reviewing the evidence for S duality of the toroidally compactiied heterotic string in 4d that was obtained in the period 1992{94. Next they review recently discovered dualities that relate all ve of the 10d superstring theories and a quantum extension of 11d supergravity called M theory. The study of p-branes of various dimensions (some of which are D-branes) plays a ce...

In this paper, we apply the methods developed in recent work for constructing A-twisted (2,2) Landau-Ginzburg models to analogous (0,2) models. In particular, we study (0,2) LandauGinzburg models on topologically non-trivial spaces away from large-radius limits, where one expects to find correlation function contributions akin to (2,2) curve corrections. Such heterotic theories admit Aand B-mod...