By looking at phase transitions which occur as parameters are varied in supersymmetric gauge theories, a natural relation is found between sigma models based on Calabi-Yau hypersurfaces in weighted projective spaces and Landau-Ginzburg models. The construction permits one to recover the known correspondence between these types of models and to greatly extend it to include new classes of manifolds and also to include models with (0, 2) world-sheet supersymmetry. The construction also predicts the possibility of certain physical processes involving a change in the topology of space-time. The present paper is based on systematically exploiting one simple idea which is familiar in N = 1 supersymmetric theories in four dimensions and which we will therefore first state in that context. We consider renormalizable gauge theories constructed from vector (gauge) multiplets and charged chiral multiplets. If the

It is argued that black hole condensation can occur at conifold singularities in the moduli space of type II Calabi-Yau string vacua. The condensate signals a smooth transition to a new Calabi-Yau space with different Euler characteristic and Hodge numbers. In this manner string theory unifies the moduli spaces of many or possibly all Calabi-Yau vacua. Elementary string states and black holes are smoothly interchanged under the transitions, and therefore cannot be invariantly distinguished. Furthermore, the transitions establish the existence of mirror symmetry for many or possibly all Calabi-Yau manifolds.

We consider supersymmetric gauge theories with impurities in various dimensions. These systems arise in the study of intersecting branes. Unlike conventional gauge theories, the Higgs branch of an impurity theory can have compact directions. For models with eight supercharges, the Higgs branch is a hyperKähler manifold given by the moduli space of solutions of certain differential equations. These equations are the dimensional reductions of self-duality equations with boundary conditions determined by the impurities. They can also be interpreted as Nahm transforms of self-duality equations on toroidally compactified spaces. We discuss the application of our results to the light-cone formulation of Yang-Mills theories and to the solution of certain N=2 d=4 gauge theories.

We study four-dimensional superconformal field theories coupled to three-dimensional superconformal boundary or defect degrees of freedom. Starting with bulk N = 2, d = 4 theories, we construct abelian models preserving N = 2, d = 3 supersymmetry and the conformal symmetries under which the boundary/defect is invariant. We write the action, including the bulk terms, in N = 2, d = 3 superspace. Moreover we derive Callan-Symanzik equations for these models using their superconformal transformation properties and show that the beta functions vanish to all orders in perturbation theory, such that the models remain superconformal upon quantization. Furthermore we study a model with N = 4 SU(N) Yang-Mills theory in the bulk coupled to a N = 4, d = 3 hypermultiplet on a defect. This model was constructed by DeWolfe, Freedman and Ooguri, and conjectured to be conformal based on its relation to an AdS configuration studied by Karch and Randall. We write this model in N = 2, d = 3 superspace, which has the distinct advantage that non-renormalization theorems become transparent. Using N = 4, d = 3 supersymmetry, we argue that the model is conformal.

Abstract. A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric sum of outer product of vectors. A rank-1 order-k tensor is the outer product of k non-zero vectors. Any symmetric tensor can be decomposed into a linear combination of rank-1 tensors, each of them being symmetric or not. The rank of a symmetric tensor is the minimal number of rank-1 tensors that is necessary to reconstruct it. The symmetric rank is obtained when the constituting rank-1 tensors are imposed to be themselves symmetric. It is shown that rank and symmetric rank are equal in a number of cases, and that they always exist in an algebraically closed field. We will discuss the notion of the generic symmetric rank, which, due to the work of Alexander and Hirschowitz, is now known for any values of dimension and order. We will also show that the set of symmetric tensors of symmetric rank at most r is not closed, unless r = 1. Key words. Tensors, multiway arrays, outer product decomposition, symmetric outer product decomposition, candecomp, parafac, tensor rank, symmetric rank, symmetric tensor rank, generic symmetric rank, maximal symmetric rank, quantics AMS subject classifications. 15A03, 15A21, 15A72, 15A69, 15A18 1. Introduction. We

In the strong-coupling limit of the heterotic string theory constructed by Hoˇrava and Witten, an 11-dimensional supergravity theory is coupled to matter multiplets confined to 10-dimensional mirror planes. This structure suggests that realistic unification models are obtained, after compactification of 6 dimensions, as theories of 5-dimensional supergravity in an interval, coupling to matter fields on 4-dimensional walls. Supersymmetry breaking may be communicated from one boundary to another by the 5-dimensional fields. In this paper, we study a toy model of this communication in which 5-dimensional super-Yang-Mills theory in the bulk couples to chiral multiplets on the walls. Using the auxiliary fields of the Yang-Mills multiplet, we find a simple algorithm for coupling the bulk and boundary fields. We demonstrate two different mechanisms for generating soft supersymmetry breaking terms in the boundary theory. We also compute the Casimir energy generated by supersymmetry breaking.

We discuss the possible cosmological implications of a class of superluminal particles, in a scenario where: a) Lorentz invariance is only an approximate property of the equations of a sector of matter; b) several critical speeds of matter in vacuum exist. The Big Bang scenario and the evolution of the very early universe, as well as large scale structure, can be strongly influenced by the new particles. 1. THE NEW PARTICLES In a recent paper [1], we proposed a new class of non-tachyonic superluminal particles assuming the existence of several critical speeds of matter in vacuum (like those of light and sound in a defectless, perfectly transparent crystal at zero temperature). Considering an analogy with sine-Gordon solitons in a galilean world, we pointed out that the apparent Lorentz invariance of the laws of physics does not imply that space-time is indeed mikowskian. Special relativity is usually presented as an intrinsic property of space-time and geometry is the startpoint of the theory of gravitation in general relativity. However, a look to various dynamical systems would suggest a more flexible view with the properties of

hep-th/0109168

Starting with the Lagrangian formalism with N = 2 supersymmetry in terms of two Grassmann variables in Classical Mechanics, the Dirac canonical quantization method is implemented. The N = 2 supersymmetry algebra is associated to one-component and two-component eigenfunctions considered in the Schrödinger picture of Nonrelativistic Quantum Mechanics. Applications are contemplated.

In this paper, we study the perturbative aspects of a twisted version of the twodimensional (0, 2) heterotic sigma model on a holomorphic gauge bundle E over a complex, hermitian manifold X. We show that the model can be naturally described in terms of the mathematical theory of “Chiral Differential Operators”. In particular, the physical anomalies of the sigma model can be reinterpreted in terms of an obstruction to a global definition of the associated sheaf of vertex superalgebras derived from the free conformal field theory describing the model locally on X. One can also obtain a novel understanding of the sigma model one-loop beta function solely in terms of holomorphic data. At the (2, 2) locus, where the obstruction vanishes for any smooth manifold X, we obtain a purely mathematical description of the half-twisted variant of the topological A-model and (if c1(X) = 0) its elliptic genus. By studying the half-twisted (2, 2) model on X = CP 1, one can show that a subset of the infinite-dimensional space of physical operators generates an underlying super-affine Lie algebra. Furthermore, on a non-Kähler, parallelised, group manifold with torsion, we uncover a direct relationship between the modulus of the corresponding sheaves of chiral de Rham complex, and the level of the underlying WZW theory.