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357
Phases of N = 2 theories in two dimensions
 NUCL. PHYS. B
, 1993
"... 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 CalabiYau hypersurfaces in weighted projective spaces and LandauGinzburg models. The construction permits one to recover the known corres ..."
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Cited by 239 (1 self)
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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 CalabiYau hypersurfaces in weighted projective spaces and LandauGinzburg 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) worldsheet supersymmetry. The construction also predicts the possibility of certain physical processes involving a change in the topology of spacetime.
A Supersymmetry Primer
, 2011
"... I provide a pedagogical introduction to supersymmetry. The level of discussion is aimed at readers who are familiar with the Standard Model and quantum field theory, but who have had little or no prior exposure to supersymmetry. Topics covered include: motivations for supersymmetry, the construction ..."
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Cited by 232 (2 self)
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I provide a pedagogical introduction to supersymmetry. The level of discussion is aimed at readers who are familiar with the Standard Model and quantum field theory, but who have had little or no prior exposure to supersymmetry. Topics covered include: motivations for supersymmetry, the construction of supersymmetric Lagrangians, superspace and superfields, soft supersymmetrybreaking interactions, the Minimal Supersymmetric Standard Model (MSSM), Rparity and its consequences, the origins of supersymmetry breaking, the mass spectrum of the MSSM, decays of supersymmetric particles, experimental signals for supersymmetry, and some extensions of the minimal framework.
Black Hole Condensation And The Unification Of String Vacua
, 1995
"... It is argued that black hole condensation can occur at conifold singularities in the moduli space of type II CalabiYau string vacua. The condensate signals a smooth transition to a new CalabiYau space with different Euler characteristic and Hodge numbers. In this manner string theory unifies the m ..."
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Cited by 164 (13 self)
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It is argued that black hole condensation can occur at conifold singularities in the moduli space of type II CalabiYau string vacua. The condensate signals a smooth transition to a new CalabiYau space with different Euler characteristic and Hodge numbers. In this manner string theory unifies the moduli spaces of many or possibly all CalabiYau 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 CalabiYau manifolds.
Symmetric tensors and symmetric tensor rank
 Scientific Computing and Computational Mathematics (SCCM
, 2006
"... 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 rank1 orderk tensor is the outer product of k nonzero vectors. An ..."
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Cited by 101 (22 self)
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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 rank1 orderk tensor is the outer product of k nonzero vectors. Any symmetric tensor can be decomposed into a linear combination of rank1 tensors, each of them being symmetric or not. The rank of a symmetric tensor is the minimal number of rank1 tensors that is necessary to reconstruct it. The symmetric rank is obtained when the constituting rank1 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
Fourdimensional superconformal theories with interacting boundaries or defects,” Phys. Rev. D66
, 2002
"... We study fourdimensional superconformal field theories coupled to threedimensional 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 ..."
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Cited by 81 (4 self)
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We study fourdimensional superconformal field theories coupled to threedimensional 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 CallanSymanzik 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) YangMills 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 nonrenormalization theorems become transparent. Using N = 4, d = 3 supersymmetry, we argue that the model is conformal.
Transmission Of Supersymmetry Breaking From A FourDimensional Boundary”, Phys. Rev. D58
, 1998
"... In the strongcoupling limit of the heterotic string theory constructed by Hoˇrava and Witten, an 11dimensional supergravity theory is coupled to matter multiplets confined to 10dimensional mirror planes. This structure suggests that realistic unification models are obtained, after compactificatio ..."
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Cited by 70 (0 self)
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In the strongcoupling limit of the heterotic string theory constructed by Hoˇrava and Witten, an 11dimensional supergravity theory is coupled to matter multiplets confined to 10dimensional mirror planes. This structure suggests that realistic unification models are obtained, after compactification of 6 dimensions, as theories of 5dimensional supergravity in an interval, coupling to matter fields on 4dimensional walls. Supersymmetry breaking may be communicated from one boundary to another by the 5dimensional fields. In this paper, we study a toy model of this communication in which 5dimensional superYangMills theory in the bulk couples to chiral multiplets on the walls. Using the auxiliary fields of the YangMills 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.
The Higgs branch of impurity theories
 Adv. Theor. Math. Phys
, 1998
"... 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 ..."
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Cited by 66 (2 self)
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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 selfduality equations with boundary conditions determined by the impurities. They can also be interpreted as Nahm transforms of selfduality equations on toroidally compactified spaces. We discuss the application of our results to the lightcone formulation of YangMills theories and to the solution of certain N=2 d=4 gauge theories.
Twocomponent spinor techniques and Feynman rules for quantum field theory and supersymmetry
, 2008
"... ..."
theory without Feynman diagrams: One loop effective actions,” Nucl. Phys. B 385
 Lett. B
, 1992
"... In this paper the connection between standard perturbation theory techniques and the new BernKosower calculational rules for gauge theory is clarified. For oneloop effective actions of scalars, Dirac spinors, and vector bosons in a background gauge field, BernKosowertype rules are derived without ..."
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Cited by 45 (0 self)
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In this paper the connection between standard perturbation theory techniques and the new BernKosower calculational rules for gauge theory is clarified. For oneloop effective actions of scalars, Dirac spinors, and vector bosons in a background gauge field, BernKosowertype rules are derived without the use of either string theory or Feynman diagrams. The effective action is written as a onedimensional path integral, which can be calculated to any order in the gauge coupling; evaluation leads to Feynman parameter integrals directly, bypassing the usual algebra required from Feynman diagrams, and leading to compact and organized expressions. This formalism is valid offshell, is explicitly gauge invariant, and can be extended to a number of other field theories.
Introductory lowenergy supersymmetry
, 1993
"... Lowenergy supersymmetry is a theoretical extension of the Standard Model of particle physics in which supersymmetry is invoked to explain the origin of the electroweak scale. In this approach, the energy scale of supersymmetry breaking can be no larger than about 1 TeV. In these lectures, a pedagog ..."
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Cited by 43 (5 self)
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Lowenergy supersymmetry is a theoretical extension of the Standard Model of particle physics in which supersymmetry is invoked to explain the origin of the electroweak scale. In this approach, the energy scale of supersymmetry breaking can be no larger than about 1 TeV. In these lectures, a pedagogical account of softly broken supersymmetric gauge theories is presented. The minimal supersymmetric extension of the Standard Model (MSSM) is defined and constraints on its parameters are explored. The implications of supersymmetric treelevel interactions and its oneloop corrections are discussed. Lowenergy supersymmetric model alternatives to the MSSM are briefly mentioned.