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Supersymmetric bosonic backgrounds governed by first-order BPS equations, can be realised in a much broader setting by relaxing the requirement of closure of the superalgebra beyond the level of quadratic fermion terms. The resulting…
The type IIB matrix model is one of the most promising candidates for a nonperturbative formulation of superstring theory. In particular, its Lorentzian version was shown to exhibit an interesting real-time dynamics such as the spontaneous…
Using the corepresentation of the quantum supergroup OSp_q(1/2) a general method for constructing noncommutative spaces covariant under its coaction is developed. In particular, a one-parameter family of covariant algebras, which may be…
We introduce a transverse field Ising model with order N^2 spins interacting via a nonlocal quartic interaction. The model has an O(N,Z), hyperoctahedral, symmetry. We show that the large N partition function admits a saddle point in which…
Neveu-Schwarz-Ramond type heterotic and type-II superstrings in four dimensional curved space-time are constructed as exact $N=1$ superconformal theories. The tachyon is eliminated with a GSO projection. The theory is based on the N=1…
We study classical field theories that do not admit an action principle, implying that their formulation is entirely in terms of equations of motion. In the theories that we consider, supersymmetry is realized on the mass-shell. We will…
We construct p-brane solutions with non-trivial world volume metrics and show that applied to supergravity theories, they will lead to threshold BPS bound states of intersecting solutions. However applied to certain specific values of the…
Vacuum structure of a quantum field theory is a crucial property. In theories with extended symmetries, such as supersymmetric gauge theories, the vacuum is typically a continuous manifold, called the vacuum moduli space, parametrized by…
We describe string-theory and $d=11$ supergravity solutions involving symmetric spaces of constant negative curvature. Many examples of non-supersymmetric string compactifications on hyperbolic spaces $H_r$ of finite volume are given in…
We suggest and motivate a precise equivalence between uncompactified eleven dimensional M-theory and the N = infinity limit of the supersymmetric matrix quantum mechanics describing D0-branes. The evidence for the conjecture consists of…
The issue of justifying the matrix-theory proposal is revisited. We first discuss how the matrix-string theory is derived directly starting from the eleven dimensional supermembrane wrapped around a circle of radius $R=g_s\ell_s$, without…
Two-dimensional $O(N)$ non-linear sigma models are exactly solvable theories and have many applications, from statistical mechanics to their use as QCD toy models. We consider a supersymmetric extension, the non-linear sigma model on the…
We derive four-dimensional effective theories for warped compactification of the ten-dimensional IIB supergravity and the eleven-dimensional Horava-Witten model. We show that these effective theories allow a much wider class of solutions…
We use non-perturbative U-duality symmetries of type II strings to construct new vacuum solutions. In some ways this generalizes the F-theory vacuum constructions. We find the possibilities of new vacuum constructions are very limited.…
Exact massive S-matrices for two dimensional sigma models on symmetric spaces SU(2N)/Sp(N) and Sp(2P)/Sp(P)*Sp(P) are conjectured. They are checked by comparison of perturbative and non perturbative TBA calculations of free energy in a…
We derive the mass formulae for ${\cal N}=1$, $D=4$ matter-coupled Supergravity for broken (and unbroken) Supersymmetry in curved space-time. These formulae are applicable to de Sitter configurations as is the case for inflation. For…
At the macrosopic level we study candidate 3D effective field theories associated to M theory in three dimensions. These represent analogs of 11D supergravity for eleven dimensional M-theory. At the microscopic level we study various world…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…
M-theory has different global supersymmetry structures in its various dual incarnations, as characterized by the M-algebra in 11D, the type IIA, type-IIB, heterotic, type-I extended supersymmetries in 10D, and non-Abelian supersymmetries in…
We construct a new supermatrix model which represents a manifestly supersymmetric noncommutative regularisation of the $UOSp(2\vert 1)$ supersymmetric Schwinger model on the supersphere. Our construction is much simpler than those already…