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A review of orbifold geometry is given, followed by a review of the construction of four-dimensional heterotic string models by compactification on a six-dimensional Z_3 orbifold. Particular attention is given to the details of the…
We study the noncommutative superspace of arbitrary dimensions in a systematic way. Superfield theories on a noncommutative superspace can be formulated in two folds, through the star product formalism and in terms of the supermatrices. We…
We analyze solutions of string theory and supergravity which involve real hyperbolic spaces. Examples of string compactifications are given in terms of hyperbolic coset spaces of finite volume $\Gamma\backslash {\mathbb H}^N$, where…
Open and Closed super-string field theories are constructed in an event-symmetric target space. The partition functions of Statistical and Quantum models are constructed in terms of invariants defined on Lie-algebra representations. An…
Starting from the primal principle based on the noncommutative nature of (9+1)-dimensional spacetime, we construct a topologically twisted version of the supersymmetric reduced model with a certain modification. Our formulation…
Retrieval of classical behaviour in quantum cosmology is usually discussed in the framework of minisuperspace models in the presence of scalar fields together with the inhomogeneous modes of gravitational or scalar fields. In this work we…
Topological supermatter is given by ordinary topological matter constrained by supersymmetry or graded supergroups such as OSP(2N|2N). Using results on super oscillators and lattice QFT$_{d}$, we construct a super tight binding model on…
The properties of the vacuum are addressed in the two- and four-dimensional quark models for QCD. It is demonstrated that the two-dimensional QCD ('t Hooft model) possesses only one possible vacuum state - the solution to the mass-gap…
By using graded (super) Lie algebras, we can construct noncommutative superspace on curved homogeneous manifolds. In this paper, we take a flat limit to obtain flat noncommutative superspace. We particularly consider $d=2$ and $d=4$…
We review several mechanisms for supersymmetry breaking in orientifold models. In particular, we focus on non-supersymmetric open-string realisations that correspond to consistent flat-space solutions of the classical equations of motion.…
We review the construction and theoretical implications of the USp(2k) matrix model in zero dimension introduced in ref. \cite{IT1,IT2}. It is argued that the model provides a constructive approach to Type I superstrings and is at the same…
We investigate orbifold and smooth Calabi-Yau compactifications of the non-supersymmetric heterotic SO(16)xSO(16) string. We focus on such Calabi-Yau backgrounds in order to recycle commonly employed techniques, like index theorems and…
Nonperturbative solutions to the nonlinear field equations in the NS sector of cubic as well as nonpolynomial superstring field theory can be obtained from a linear equation which includes a "spectral" parameter \lambda and a coboundary…
The IKKT model is a promising candidate for a non-perturbative description of Type IIB superstring theory. It is known from analytic approaches and numerical simulations that the IKKT matrix model with a mass term admits interesting…
A Newtonian matrix cosmology, correspoding to the BFSS model of eleven-dimensional M-theory in the IMF as a (0+1) M(atrix) model is constructed. Interesting new results are obtained, such as the existence of (much sought for in the past)…
We show that there exist some intimate connections between three unconventional Schr\"odinger equations based on the use of deformed canonical commutation relations, of a position-dependent effective mass or of a curved space, respectively.…
Let group generators having finite-dimensional representation be realized as Hermitian linear differential operators without nhomogeneous terms as takes place, for example, for the SO(n) group. Then orresponding group Hamiltonians…
We consider the Skyrme model using the explicit parameterization of the rotation group SO(3) through elements of its algebra. Topologically nontrivial solutions already arise even in the one-dimensional case because the fundamental group of…
We review the construction of open descendants of the type IIB superstring on the Z-orbifold. It results in a chiral four-dimensional model with gauge group $SO(8) \otimes U(12)$ and three generations of matter in the $(8,12^*)\oplus…
We propose a matrix model on a homogeneous plane-wave background with 20 supersymmetries. This background is anti-Mach type and is equivalent to the time-dependent background. We study supersymmetries in this theory and calculate the…