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791
Sduality and noncommutative gauge theory
 JHEP
, 2000
"... It is conjectured that strongly coupled, spatially noncommutative N = 4 YangMills theory has a dual description as a weakly coupled open string theory in a near critical electric field, and that this dual theory is fully decoupled from closed strings. Evidence for this conjecture is given by the ab ..."
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Cited by 119 (2 self)
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It is conjectured that strongly coupled, spatially noncommutative N = 4 YangMills theory has a dual description as a weakly coupled open string theory in a near critical electric field, and that this dual theory is fully decoupled from closed strings. Evidence for this conjecture is given by the absence of physical closed string poles in the nonplanar oneloop open string diagram. The open string theory can be viewed as living in a geometry
TOPOLOGICAL STRINGS ON NONCOMMUTATIVE MANIFOLDS
, 2003
"... We identify a deformation of the N = 2 supersymmetric sigma model on a CalabiYau manifold X which has the same effect on Bbranes as a noncommutative deformation of X. We show that for hyperkähler X such deformations allow one to interpolate continuously between the Amodel and the Bmodel. For ge ..."
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Cited by 97 (8 self)
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We identify a deformation of the N = 2 supersymmetric sigma model on a CalabiYau manifold X which has the same effect on Bbranes as a noncommutative deformation of X. We show that for hyperkähler X such deformations allow one to interpolate continuously between the Amodel and the Bmodel. For generic values of the noncommutativity and the Bfield, properties of the topologically twisted sigmamodels can be described in terms of generalized complex structures introduced by N. Hitchin. For example, we show that the path integral for the deformed sigmamodel is localized on generalized holomorphic maps, whereas for the Amodel and the Bmodel it is localized on holomorphic and constant maps, respectively. The geometry of topological Dbranes is also best described using generalized complex structures. We also derive a constraint on the Chern character of topological Dbranes, which includes Abranes and Bbranes as special cases.
Noncommutative worldvolume geometries
 Branes on SU(2) and fuzzy spheres, JHEP 09
, 1999
"... The geometry of Dbranes can be probed by open string scattering. If the background carries a nonvanishing Beld, the worldvolume becomes noncommutative. Here we explore the quantization of worldvolume geometries in a curved background with nonzero NeveuSchwarz 3form eld strength H = dB. Usin ..."
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Cited by 85 (9 self)
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The geometry of Dbranes can be probed by open string scattering. If the background carries a nonvanishing Beld, the worldvolume becomes noncommutative. Here we explore the quantization of worldvolume geometries in a curved background with nonzero NeveuSchwarz 3form eld strength H = dB. Using exact and generally applicable methods from boundary conformal eld theory, we study the example of open strings in the SU(2) WessZuminoWitten model, and establish a relation with fuzzy spheres or certain (nonassociative) deformations thereof. These ndings could be of direct relevance for Dbranes in the presence of NeveuSchwarz 5branes; more importantly, they provide insight into a completely new class of worldvolume geometries.
Unstable solitons in noncommutative gauge theory
"... We find a class of exact solutions of noncommutative gauge theories corresponding to unstable nonBPS solitons. In the twodimensional euclidean (or 2+1 dimensional lorentzian) U(1) theory we find localized solutions carrying nonzero magnetic flux. In four euclidean dimensions we find nonBPS soluti ..."
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Cited by 72 (1 self)
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We find a class of exact solutions of noncommutative gauge theories corresponding to unstable nonBPS solitons. In the twodimensional euclidean (or 2+1 dimensional lorentzian) U(1) theory we find localized solutions carrying nonzero magnetic flux. In four euclidean dimensions we find nonBPS solutions with the same Pontrjagin charge but greater energy than the usual selfdual YangMills instanton. We conjecture that these solutions and generalizations thereof correspond to nonsupersymmetric configurations of D(p − 2k) branes (or intersections thereof) in a Dp brane in the noncommutative scaling limit of large Bfield. In the particular case of a 0brane on a 2brane the analysis of small fluctuations reveals an infinite tower of states which agrees exactly with that of the 0 − 2 CFT in the scaling limit. The spectrum contains a tachyon, and we show explicitly that
The Cdeformation of gluino and nonplanar diagrams
 Adv. Theor. Math. Phys
"... We consider a deformation of N = 1 supersymmetric gauge theories in four dimensions, which we call the Cdeformation, where the gluino field satisfies a Cliffordlike algebra dictated by a selfdual twoform, instead of the standard Grassmannian algebra. The superpotential of the deformed gauge theo ..."
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Cited by 64 (1 self)
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We consider a deformation of N = 1 supersymmetric gauge theories in four dimensions, which we call the Cdeformation, where the gluino field satisfies a Cliffordlike algebra dictated by a selfdual twoform, instead of the standard Grassmannian algebra. The superpotential of the deformed gauge theory is computed by the full partition function of an associated matrix model (or more generally a bosonic gauge theory), including nonplanar diagrams. In this identification, the strength of the twoform controls the genus expansion of the matrix model partition function. For the case of pure N = 1 YangMills this deformation leads to the identification of the all genus partition function of c = 1 noncritical bosonic string at selfdual radius as the glueball superpotential. Though the Cdeformation violates Lorentz invariance, the deformed Fterms are Lorentz invariant and the Lorentz violation is screened in the IR. 1
The standard model on noncommutative spacetime
 PHYS. J. C23
"... We consider the Standard Model on a noncommutative space and expand the action in the noncommutativity parameter θ µν. No new particles are introduced, the structure group is SU(3) × SU(2) × U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary Standard ..."
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Cited by 62 (5 self)
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We consider the Standard Model on a noncommutative space and expand the action in the noncommutativity parameter θ µν. No new particles are introduced, the structure group is SU(3) × SU(2) × U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary Standard Model. At leading order in θ µν we find new vertices which are absent in the Standard Model on commutative spacetime. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in noncommutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the
Quantized Gauge Theory on the Fuzzy Sphere as Random
 Matrix Model, Nucl. Phys. B679
, 2004
"... Gauge theories provide the best known description of the fundamental forces in nature. At very short distances however, physics is not known, and it seems unlikely that spacetime is a perfect continuum down to arbitrarily small scales. Indeed, physicists have started to learn in recent years how to ..."
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Cited by 60 (16 self)
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Gauge theories provide the best known description of the fundamental forces in nature. At very short distances however, physics is not known, and it seems unlikely that spacetime is a perfect continuum down to arbitrarily small scales. Indeed, physicists have started to learn in recent years how to formulate field
Exact solution of quantum field theory on noncommutative phase spaces
 017, 2004, hepth/0308043. – 43
"... We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the GroenewoldMoyal starproduct. Explicit results are presented for all Green’s fun ..."
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Cited by 59 (6 self)
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We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the GroenewoldMoyal starproduct. Explicit results are presented for all Green’s functions in arbitrary even spacetime dimensionality. Various scaling limits of the field theory are analysed nonperturbatively and the renormalizability of each limit examined. A supersymmetric extension of the field theory is also constructed in which the supersymmetry transformations are parametrized by differential operators in an infinitedimensional noncommutative algebra.
GromovHausdorff distance for quantum metric spaces
 Mem. Amer. Math. Soc
"... Abstract. By a quantum metric space we mean a C ∗algebra (or more generally an orderunit space) equipped with a generalization of the usual Lipschitz seminorm on functions which one associates to an ordinary metric. We develop for compact quantum metric spaces a version of Gromov–Hausdorff distanc ..."
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Cited by 57 (7 self)
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Abstract. By a quantum metric space we mean a C ∗algebra (or more generally an orderunit space) equipped with a generalization of the usual Lipschitz seminorm on functions which one associates to an ordinary metric. We develop for compact quantum metric spaces a version of Gromov–Hausdorff distance. We show that the basic theorems of the classical theory have natural quantum analogues. Our main example involves the quantum tori, Aθ. We show, for consistently defined “metrics”, that if a sequence {θn} of parameters converges to a parameter θ, then the sequence {Aθn} of quantum tori converges in quantum Gromov–Hausdorff distance to Aθ. 1.