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This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…
We study the couplings of discrete states that appear in the string theory embedded in two dimensions, and show that they are given by the structure constants of the group of area preserving diffeomorphisms. We propose an effective action…
In the presence of a static quark--antiquark pair, the spectrum of the low-lying states in SU($N$) gauge theories is discrete and likely to be described, at large quark separations $r$, by an effective string theory. The expansion of the…
A particular two-parameter class of little string theories can be described by $M$ parallel M5-branes probing a transverse affine $A_{N-1}$ singularity. We previously discussed the duality between the theories labelled by $(N,M)$ and…
In this work cosmological models are considered for the low energy string cosmological effective action (tree level) in the absence of dilaton potential. A two parametric non-diagonal family of analytic solutions is found. The curvature is…
Long strings emerge in many Quantum Field Theories, for example as vortices in Abelian Higgs theories, or flux tubes in Yang-Mills theories. The actions of such objects can be expanded in the number of derivatives, around a long straight…
These lecture notes provide a short review of the status of time dependent backgrounds in String theory, and in particular those that contain space-like singularities. Despite considerable efforts, we do not have yet a full and compelling…
1. Preliminaries. 2. Heterotic string and motivations for large volume compactifications; 2.1 Gauge coupling unification; 2.2 Supersymmetry breaking by compactification. 3. M-theory on S^1/Z_2 \times Calabi-Yau. 4. Type I/I' string theory…
In the strong coupling limit type IIA superstring theory develops an eleventh dimension that is not apparent in perturbation theory. This suggests the existence of a consistent 11d quantum theory, called M theory, which is approximated by…
We analyze properties of the Sp(2M) conformally invariant field equations in the recently proposed generalized $\half M(M+1)$-dimensional space-time $\M_M$ with matrix coordinates. It is shown that classical solutions of these field…
We present a critical review and summary of String Gas Cosmology. We include a pedagogical derivation of the effective action starting from string theory, emphasizing the necessary approximations that must be invoked. Working in the…
We consider string theory in a time dependent orbifold with a null singularity. The singularity separates a contracting universe from an expanding universe, thus constituting a big crunch followed by a big bang. We quantize the theory both…
We study time-dependent backgrounds in the low energy regimes of string theories. In particular the emphasis is on the general study of exotic phenomena such as positive acceleration and gravitational bounces. We generalize the usual…
We argue that the space-time uncertainty relation of the form $\Delta X \Delta T \gtrsim \alpha'$ for the observability of the distances with respect to time, $\Delta T$, and space, $\Delta X$, is universally valid in string theory…
The four-dimensional superstring solutions define at low energy effective supergravity theories. A class of them extends successfully the validity of the standard model up to the string scale (${\cal O}(10^{17})~TeV$). We stress the…
We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces…
The dynamics of heavy quarkonium systems in the strong coupling regime reduces to a quantum mechanical problem with a number of potentials which may be organized in powers of 1/m, m being the heavy quark mass. The potentials must be…
We illustrate the various ways in which the algebraic framework of noncommutative geometry naturally captures the short-distance spacetime properties of string theory. We describe the noncommutative spacetime constructed from a vertex…
A method to solve various aspects of the strong coupling expansion of the superconformal field theory duals of AdS_5 x X geometries from first principles is proposed. The main idea is that at strong coupling the configurations that dominate…
We present a general analysis of the thermodynamics of spinning black p-branes of string and M-theory. This is carried out both for the asymptotically-flat and near-horizon case, with emphasis on the latter. In particular, we use the…