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63
Holomorphic anomaly in gauge theories and matrix models
, 2006
"... We use the holomorphic anomaly equation to solve the gravitational corrections to SeibergWitten theory and a twocut matrix model, which is related by the DijkgraafVafa conjecture to the topological Bmodel on a local CalabiYau manifold. In both cases we construct propagators that give a recursiv ..."
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Cited by 36 (12 self)
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We use the holomorphic anomaly equation to solve the gravitational corrections to SeibergWitten theory and a twocut matrix model, which is related by the DijkgraafVafa conjecture to the topological Bmodel on a local CalabiYau manifold. In both cases we construct propagators that give a recursive solution in the genus modulo a holomorphic ambiguity. In the case of SeibergWitten theory the gravitational corrections can be expressed in closed form as quasimodular functions of Γ(2). In the matrix model we fix the holomorphic ambiguity up to genus two. The latter result establishes the DijkgraafVafa conjecture at that genus and yields a new method for solving the matrix model at fixed genus in closed form in terms of generalized hypergeometric functions.
Towards the Quantum Geometry of the M5brane in a Constant CField from Multiple Membranes
, 2009
"... A We show that the Nahm equation which describes a fuzzy D3brane in the presence of a Bfield can be derived as a boundary condition of the F1strings ending on the D3brane, and that the modifications of the original Nahm equation by a Bfield can be understood in terms of the noncommutative geome ..."
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Cited by 30 (10 self)
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A We show that the Nahm equation which describes a fuzzy D3brane in the presence of a Bfield can be derived as a boundary condition of the F1strings ending on the D3brane, and that the modifications of the original Nahm equation by a Bfield can be understood in terms of the noncommutative geometry of the D3brane. Naturally this is consistent with the alternative derivation by quantising the open strings in the Bfield background. We then consider a configuration of multiple M2branes ending on an M5brane with a constant 3form Cfield. By analogy with the case of strings ending on a D3brane with a constant Bfield, one can expect that this system can be described in terms of the boundary of the M2branes moving within a certain kind of quantum geometry on the M5brane worldvolume. By repeating our analysis, we show that the analogue of the Bfield modified Nahm equation, the Cfield modified BasuHarvey equation can also be understood as a boundary condition of the M2branes. We then compare this to the M5brane BIon description and show that the two descriptions match provided we postulate a new type of quantum geometry on the M5brane worldvolume. Unlike the Dbrane case,
Fuzzy CP (nm) as a quantum superspace
 Proceedings of the Workshop on Symmetries in Gravity and Field Theory: In Honor of Prof. J.A. de Azcarraga
, 2003
"... hepth/0311159 ..."
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N = 2 supersymmetric U(1) gauge theory in noncommutative harmonic superspace
 Lett
"... We study N = 2 supersymmetric U(1) gauge theory in the noncommutative harmonic superspace with nonanticommutative fermionic coordinates. We examine the gauge transformation which preserves the WessZumino gauge by harmonic expansions of component fields. The gauge transformation is shown to depend o ..."
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Cited by 12 (0 self)
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We study N = 2 supersymmetric U(1) gauge theory in the noncommutative harmonic superspace with nonanticommutative fermionic coordinates. We examine the gauge transformation which preserves the WessZumino gauge by harmonic expansions of component fields. The gauge transformation is shown to depend on the deformation parameters and the antiholomorphic scalar field. We compute the action explicitly up to the third order in component fields and discuss the field Field theories on noncommutative superspace[1] have been taken much attentions recently. In superstring theory, they correspond to the field theories on the Dbranes in the graviphoton background[2]. The RamondRamond fields induces the non(anti)commutativity for the worldsheet fermionic fields in the hybrid formalism of superstrings [2, 3, 4]. When
Geometric transitions, flops and nonKähler manifolds: I
, 2004
"... We construct a duality cycle which provides a complete supergravity description of geometric transitions in type II theories via a flop in Mtheory. This cycle connects the different supergravity descriptions before and after the geometric transitions. Our construction reproduces many of the known p ..."
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Cited by 11 (6 self)
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We construct a duality cycle which provides a complete supergravity description of geometric transitions in type II theories via a flop in Mtheory. This cycle connects the different supergravity descriptions before and after the geometric transitions. Our construction reproduces many of the known phenomena studied earlier in the literature and allows us to describe some new and interesting aspects in a simple and elegant fashion. A precise supergravity description of new torsional manifolds that appear on the type IIA side with branes and fluxes and the corresponding geometric transition are obtained. A local description of new G2 manifolds that are circle fibrations over nonKähler manifolds
Dbrane instantons and matrix models
, 2008
"... We point out that in some situations it is possible to use matrix model techniques a la DijkgraafVafa to perturbatively compute Dbrane instanton effects. This provides an explanation in terms of stringy instantons of the results in hepth/0311181. We check this proposal in some simple scenarios. W ..."
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Cited by 8 (1 self)
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We point out that in some situations it is possible to use matrix model techniques a la DijkgraafVafa to perturbatively compute Dbrane instanton effects. This provides an explanation in terms of stringy instantons of the results in hepth/0311181. We check this proposal in some simple scenarios. We point out some interesting consequences of this observation, such as the fact that it gives a perturbative way of computing stringy multiinstanton effects. It also provides a further interpretation of Dbrane instantons as residual instantons of higgsed supergroups.
Hybrid Formalism, Supersymmetry Reduction, and Ramondramond Fluxes
, 2006
"... The supersymmetric hybrid formalism for Type II strings is used to study partial supersymmetry breaking in four and three dimensions. We use worldsheet techniques to derive effects of internal RamondRamond fluxes such as torsions, superpotentials and warping. ..."
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Cited by 7 (2 self)
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The supersymmetric hybrid formalism for Type II strings is used to study partial supersymmetry breaking in four and three dimensions. We use worldsheet techniques to derive effects of internal RamondRamond fluxes such as torsions, superpotentials and warping.
Nonanticommutative deformations of N=(1,1) supersymmetric theories, Theor
 Math. Phys
, 2005
"... We discuss chiralitypreserving nilpotent deformations of fourdimensional N=(1,1) Euclidean harmonic superspace and their implications in N=(1,1) supersymmetric gauge and hypermultiplet theories, basically following [hepth/0308012] and [hepth/0405049]. For the SO(4)×SU(2) invariant deformation, w ..."
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Cited by 7 (2 self)
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We discuss chiralitypreserving nilpotent deformations of fourdimensional N=(1,1) Euclidean harmonic superspace and their implications in N=(1,1) supersymmetric gauge and hypermultiplet theories, basically following [hepth/0308012] and [hepth/0405049]. For the SO(4)×SU(2) invariant deformation, we present nonanticommutative Euclidean analogs of the N=2 gauge multiplet and hypermultiplet offshell actions. As a new result, we consider a specific nonanticommutative hypermultiplet model with N=(1,0) supersymmetry. It involves free scalar fields and interacting righthanded spinor fields. Submitted to Proceedings of the Seminar “Classical and Quantum Integrable Systems” In recent years, non(anti)commutative deformations of supersymmetric field theories received a great deal of attention. The simplest type of noncommutativity affects the spacetime coordinates
Singlet deformation and non(anti)commutative N = 2 supersymmetric U(1) gauge theory, Phys
 Lett. B 595
, 2005
"... We study N = 2 supersymmetric U(1) gauge theory in non(anti)commutative N = 2 harmonic superspace with the singlet deformation, which preserves chirality. We construct a Lagrangian which is invariant under both the deformed gauge and supersymmetry transformations. We find the field redefinition such ..."
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Cited by 5 (0 self)
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We study N = 2 supersymmetric U(1) gauge theory in non(anti)commutative N = 2 harmonic superspace with the singlet deformation, which preserves chirality. We construct a Lagrangian which is invariant under both the deformed gauge and supersymmetry transformations. We find the field redefinition such that the N = 2 vector multilplet transforms canonically under the deformed symmetries. Non(anti)commutative superspace[1] with nonanticommutativity in Grassmann odd coordinates appears in superstrings compactified on CalabiYau threefold in the graviphoton background [2, 3, 4]. The lowenergy effective theory on the Dbrane is realized by supersymmetric gauge theories in non(anti)commutative superspace. Perturabative and nonperturabative aspects of these gauge theories have been studied extensively[5, 6, 7, 8]. It is an interesting problem to study the deformation of extended superspace since it admits a variety of deformation parameters[9]. The deformation of extended superspace has
Flux Vacua and Supermanifolds
, 2006
"... As been recently pointed out, physically relevant models derived from string theory require the presence of nonvanishing form fluxes besides the usual geometrical constraints. In the case of NSNS fluxes, the Generalized Complex Geometry encodes these informations in a beautiful geometrical structu ..."
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Cited by 4 (1 self)
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As been recently pointed out, physically relevant models derived from string theory require the presence of nonvanishing form fluxes besides the usual geometrical constraints. In the case of NSNS fluxes, the Generalized Complex Geometry encodes these informations in a beautiful geometrical structure. On the other hand, the RR fluxes call for supergeometry as the underlying mathematical framework. In this context, we analyze the possibility of constructing interesting supermanifolds recasting the geometrical data and RR fluxes. To characterize these supermanifolds we have been guided by the fact topological strings on supermanifolds require the superRicci flatness of the target space. This can be achieved by adding to a given bosonic manifold enough anticommuting coordinates and new constraints on the bosonic submanifold. We study these constraints at the linear and nonlinear level for a pure geometrical setting and in the presence of pform field strengths. We find that certain spaces admit several superextensions and we give a parameterization in a simple case of d bosonic coordinates and two fermionic coordinates. In addition, we comment on the role of the RR field in the construction of the supermetric. We give several examples based on supergroup manifolds and coset supermanifolds.