[en] We consider type IIA compactification on K3. We show that the instanton subsectors of the worldvolume of N 4-branes wrapped around K3 lead to a Hagedorn density of BPS states in accord with heterotic-type IIA duality in 6 dimensions. We also find evidence that the correct framework to understand the results of Nakajima on the appearance of affine Kac-Moody algebras on the cohomology of moduli space of instantons on ALE spaces is in the context of heterotic-type IIA string duality. (orig.)

[en] I review some recent developments in type I superstring theory in the context of type I-heterotic duality. In particular, I discuss the determination of type I prepotentials and the relation to their heterotic counterparts. I emphasize the existence of open string states that enhance the gauge group beyond what is naively expected from heterotic perturbation theory. (orig.)

[en] We investigate the NBI matrix model with the potential $X/Λ+X^-1+(2/η+1)/log X$ recently proposed to describe IIB superstrings. With the proper normalization, using Virasoro constraints, we prove the equivalence of this model and the Kontsevich matrix model for $/η/ne0$ and find the explicit transformation between the two models. (author)

[en] We examine the problem of generation mixing in realistic superstring derived standard-like models, constructed in the free fermionic formulation. We study the possible sources of family mixing in these models. In a specific model we estimate the Cabibbo angle. We argue that a Cabibbo angle of the correct order of magnitude can be obtained in these models. (author)

[en] We review here some of the checks of string-string duality between N = 2, D = 4 heterotic and type II models. The heterotic low energy field theory is reproduced on the type II side. It is also shown to be a generalization in the string context of the rigid N = 2 Yang-Mills theory of Seiberg and Witten which is exactly known. The non perturbative information of this rigid theory is then recovered on the type II side. This talk is based on work done in collaboration with I. Antoniadis. (orig.)

[en] We construct several examples where duality transformation commutes with the orbifolding procedure even when the orbifolding group does not act freely, and there are massless states from the twisted sector at a generic point in the moduli space. Often the matching of spectrum in the dual theories is a result of nontrivial identities satisfied by the coefficients of one loop tadpoles in the heterotic, type II and type I string theories. (orig.)

[en] We construct a Landau-Ginzburg model with the same data and symmetries as a Z₂ x Z₂ orbifold that corresponds to a class of realistic free-fermion models. Within the class of interest, we show that this orbifolding connects between different Z₂ x Z₂ orbifold models and connects with the mirror symmetry. Our work suggests that duality symmetries previously discussed in the context of specific M and F theory compactifications may be extended to the special Z₂ x Z₂ orbifold that characterizes realistic free-fermion models

[en] A recent paper by Moore and Witten explained that Ramond-Ramond fields in Type II superstring theory have a global meaning in K-theory. In this note we amplify and generalize some points raised in that paper. In particular, we express the coupling of the Ramond-Ramond fields to D-branes in a K-theoretic framework and show that the anomaly in this coupling exactly cancels the anomaly from the fermions on the brane, both in Type IIA and Type IIB. (author)

[en] This paper proposes random matrix models which have N = 1/2 supersymmetry in zero dimension. The supersymmetry breaks down spontaneously. It is shown that the double scaling limit can be defined in these models and the breakdown of the supersymmetry remains in the continuum limit. The exact non-trivial partition functions of the string theories corresponding to these matrix models are also obtained

[en] We review the macroscopic and microscopic properties of black holes of toroidally compactified heterotic and type II string theory in dimensions 4≤D≤9. General charged rotating black hole solutions are obtained by acting on a generating solution with classical duality symmetries. In D = 4, D 5 and 6≤D≤9, the generating solution for both toroidally compactified type II and heterotic strings is specified by the ADM mass, [(D-1)/2]-angular momentum components and five, three and two charges, respectively. We give the Bekenstein-Hawking entropy for these solutions, address the BPS-saturated limit and compare the results to calculations of the microscopic entropy both in the NS-NS sector and the R-R sector of the theory. We also interpret such black hole solutions as dimensionally reduced intersecting p-branes of M-theory. (orig.)