Showing papers on "Supersymmetric gauge theory published in 2003"
26 Jun 2003
TL;DR: In this paper, the authors investigated various representations for this partition function: a statistical sum over random partitions, a partition function of the ensemble of random curves, and a free fermion correlator.
Abstract: We study \( \mathcal{N} = 2 \) supersymmetric four-dimensional gauge theories, in a certain 525-02 = 2 supergravity background, called theΩ-background. The partition function of the theory in the Ω-background can be calculated explicitly. We investigate various representations for this partition function: a statistical sum over random partitions, a partition function of the ensemble of random curves, and a free fermion correlator.
1,350 citations
TL;DR: In this paper, the authors show that the transverse momentum-dependent parton distributions in the light-cone gauge contain factorizable final state interaction effects originating from the fast-moving struck quark interacting with the target spectators in deeply inelastic scattering.
454 citations
TL;DR: In this paper, the authors derived the DGLAP and BFKL evolution equations in the N = 4 supersymmetric gauge theory in the next-to-leading approximation.
423 citations
TL;DR: In this paper, a comparison of the dynamical energy spectrum of rotating closed strings in AdS5 ×S 5 and the scaling weights of the corresponding non-near-BPS operators in planar N = 4 supersymmetric gauge theory was made.
Abstract: We extend recent remarkable progress in the comparison of the dynamical energy spectrum of rotating closed strings in AdS5 ×S 5 and the scaling weights of the corresponding non-near-BPS operators in planar N = 4 supersymmetric gauge theory. On the string side the computations are feasible, using semiclassical methods, if angular momentum quantum numbers are large. This results in a prediction of gauge theory anomalous dimensions to all orders in the ‘t Hooft coupling λ. On the gauge side the direct computation of these dimensions is feasible, using a recently discovered relation to integrable (super) spin chains, provided one considers the lowest order in λ. This oneloop computation then predicts the small-tension limit of the string spectrum for all (i.e. small or large) quantum numbers. In the overlapping window of large quantum numbers and small effective string tension, the string theory and gauge theory results are found to match in a mathematically highly nontrivial fashion. In particular, we compare energies of states with (i) two large angular momenta in S 5 , and (ii) one large angular momentum in AdS5 and S 5 each, and show that the solutions are related by an analytic continuation. Finally, numerical evidence is presented on the gauge side that the agreement persists also at higher (two) loop order.
306 citations
TL;DR: In this article, the standard four dimensional superspace is deformed by making the odd coordinates $\theta$ not anticommuting, but satisfying a Clifford algebra, which determines the other commutation relations of the coordinates.
Abstract: We deform the standard four dimensional $\N=1$ superspace by making the odd coordinates $\theta$ not anticommuting, but satisfying a Clifford algebra. Consistency determines the other commutation relations of the coordinates. In particular, the ordinary spacetime coordinates $x$ cannot commute. We study chiral superfields and vector superfields and their interactions. As in ordinary noncommutative field theory, a change of variables allows us to express the gauge interactions in terms of component fields which are subject to standard gauge transformation laws. Unlike ordinary noncommutative field theories, the change of the Lagrangian is a polynomial in the deformation parameter. Despite the deformation, the noncommutative theories still have an antichiral ring with all its usual properties. We show how these theories with precisely this deformation arise in string theory in a graviphoton background.
299 citations
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TL;DR: In this paper, it was shown that BPS correlation functions in the N = 2 supersymmetric gauge theories are described by an auxiliary two-dimensional conformal field theory, which coincides with the tau-function of the Toda lattice hierarchy.
Abstract: We present new evidence for the conjecture that BPS correlation functions in the N=2 supersymmetric gauge theories are described by an auxiliary two dimensional conformal field theory. We study deformations of the N=2 supersymmetric gauge theory by all gauge-invariant chiral operators. We calculate the partition function of the N=2 theory on R^4 with appropriately twisted boundary conditions. For the U(1) theory with instantons (either noncommutative, or D-instantons, depending on the construction) the partition function has a representation in terms of the theory of free fermions on a sphere, and coincides with the tau-function of the Toda lattice hierarchy. Using this result we prove to all orders in string loop expansion that the effective prepotential (for U(1) with all chiral couplings included) is given by the free energy of the topological string on CP^1. Gravitational descendants play an important role in the gauge fields/string correspondence. The dual string is identified with the little string bound to the fivebrane wrapped on the two-sphere. We also discuss the theory with fundamental matter hypermultiplets.
268 citations
TL;DR: In this paper, the Yang-Mills Lagrangian and heavy-to-light transition currents were extended to second order in the power expansion, paying particular attention to the field redefinitions that lead to the gauge symmetries of the effective Lagrangians.
268 citations
TL;DR: In this paper, the authors study theoretical and experimental constraints on electroweak theories including a new color-singlet and electrically neutral gauge boson, and derive bounds on the mass and couplings imposed by direct production and Z-pole measurements.
Abstract: We study theoretical and experimental constraints on electroweak theories including a new color-singlet and electrically neutral gauge boson. We first note that the electric charges of the observed fermions imply that any such ${Z}^{\ensuremath{'}}$ boson may be described by a gauge theory in which the Abelian gauge groups are the usual hypercharge along with another $U(1)$ component in a kinetic-diagonal basis. Assuming that the observed quarks and leptons have generation-independent $U(1)$ charges, and that no new fermions couple to the standard model gauge bosons, we find that their $U(1)$ charges form a two-parameter family consistent with anomaly cancellation and viable fermion masses, provided there are at least three right-handed neutrinos. We then derive bounds on the ${Z}^{\ensuremath{'}}$ mass and couplings imposed by direct production and Z-pole measurements. For generic charge assignments and a gauge coupling of electromagnetic strength, the strongest lower bound on the ${Z}^{\ensuremath{'}}$ mass comes from Z-pole measurements, and is of the order of 1 TeV. If the new $U(1)$ charges are proportional to $B\ensuremath{-}L,$ however, there is no tree-level mixing between the Z and ${Z}^{\ensuremath{'}},$ and the best bounds come from the absence of direct production at CERN LEP II and the Fermilab Tevatron. If the $U(1)$ gauge coupling is one or two orders of magnitude below the electromagnetic one, these bounds are satisfied for most values of the ${Z}^{\ensuremath{'}}$ mass.
243 citations
TL;DR: In this article, the Higgs fields arise from extra-dimensional components of higher-dimensional gauge fields and quarks and leptons are introduced in the bulk, giving Yukawa couplings without conflicting with higher dimensional gauge invariance.
220 citations
TL;DR: In this paper, a supersymmetric Yang-Mills theory in two dimensions was formulated, and the lattice action respects one exact supersymmetry, which allows the target theory to emerge in the continuum limit without fine-tuning.
Abstract: We formulate a euclidean spacetime lattice whose continuum limit is (2,2) supersymmetric Yang-Mills theory in two dimensions, a theory which possesses four supercharges and an anomalous global chiral symmetry. The lattice action respects one exact supersymmetry, which allows the target theory to emerge in the continuum limit without fine-tuning. Our method exploits an orbifold construction described previously for spatial lattices in Minkowski space, and can be generalized to more complicated theories with additional supersymmetry and more spacetime dimensions.
211 citations
TL;DR: In this paper, the topological string amplitudes of N = 1 and N = 2 supersymmetric gauge theories are derived from topological strings and used to check a conjecture of Nekrasov concerning these gravitational couplings in Seiberg-Witten theory.
Abstract: Gravitational corrections in N = 1 and N = 2 supersymmetric gauge theories are obtained from topological string amplitudes. We show how they are recovered in matrix model computations. This provides a test of the proposal by Dijkgraaf and Vafa beyond the planar limit. Both, matrix model and topological string theory, are used to check a conjecture of Nekrasov concerning these gravitational couplings in Seiberg-Witten theory. Our analysis is performed for those gauge theories which are related to the cubic matrix model, i.e. pure SU(2) Seiberg-Witten theory and N = 2 U(N) SYM broken to N = 1 via a cubic superpotential. We outline the computation of the topological amplitudes for the local Calabi-Yau manifolds which are relevant for these two cases.
TL;DR: The complete set of two-loop renormalization group equations in general gauge field theories is presented in this article, including the $\ensuremath{\beta}$ functions of parameters with and without a mass dimension.
Abstract: The complete set of two-loop renormalization group equations in general gauge field theories is presented. This includes the $\ensuremath{\beta}$ functions of parameters with and without a mass dimension.
TL;DR: In this article, the phase structure of = 1 super Yang-Mills theory with SU(Nc), a chiral superfield in the adjoint, and Nf chirality superfields in the fundamental representation of the gauge group was studied.
Abstract: We use recent results of Intriligator and Wecht [1] to study the phase structure of = 1 super Yang-Mills theory with gauge group SU(Nc), a chiral superfield in the adjoint, and Nf chiral superfields in the fundamental representation of the gauge group. Our discussion sheds new light on [1] and supports the conjecture that the central charge a decreases under RG flows and is non-negative in unitary four dimensional conformal field theories.
TL;DR: In this article, the chiral ring of the gluino fields is deformed by the supergravity fields, generalizing the C-deformation which was recently introduced. But understanding the gravity corrections to the F-terms requires a non-traditional interpretation of these identities.
Abstract: We study F-terms describing coupling of the supergravity to N = 1 supersymmetric gauge theories which admit large N expansions. We show that these F-terms are given by summing over genus one non-planar diagrams of the large N expansion of the associated matrix model (or more generally bosonic gauge theory). The key ingredient in this derivation is the observation that the chiral ring of the gluino fields is deformed by the supergravity fields, generalizing the C-deformation which was recently introduced. The gravity induced part of the C-deformation can be derived from the Bianchi identities of the supergravity, but understanding gravitational corrections to the F-terms requires a non-traditional interpretation of these identities.
TL;DR: In this article, the authors generalise the formalism of differential forms to allow the discussion of arbitrary gauge fields in higher dimensions, and present the gauge symmetries, field strengths, field equations and actions for the free theory, and construct the various dual theories.
Abstract: Gauge fields in exotic representations of the Lorentz group in D dimensions – ie ones which are tensors of mixed symmetry corresponding to Young tableaux with arbitrary numbers of rows and columns – naturally arise through massive string modes and in dualising gravity and other theories in higher dimensions We generalise the formalism of differential forms to allow the discussion of arbitrary gauge fields We present the gauge symmetries, field strengths, field equations and actions for the free theory, and construct the various dual theories In particular, we discuss linearised gravity in arbitrary dimensions, and its two dual forms
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TL;DR: In this paper, the full holomorphic geometry of local Calabi-Yau threefold compactifications with N=1 supersymmetry can be obtained from matrix models, and it is shown how to connect 4+k dimensional supersymmetric theories to a k-dimensional internal bosonic gauge theory, generalizing the relation between 4d theories and matrix models.
Abstract: We show how the full holomorphic geometry of local Calabi-Yau threefold compactifications with N=1 supersymmetry can be obtained from matrix models. In particular for the conifold geometry we relate F-terms to the general amplitudes of c=1 non-critical bosonic string theory, and express them in a quiver or, equivalently, super matrix model. Moreover we relate, by deconstruction, the uncompactified c=1 theory to the six-dimensional conformal (2,0) theory. Furthermore, we show how we can use the idea of deconstruction to connect 4+k dimensional supersymmetric gauge theories to a k-dimensional internal bosonic gauge theory, generalizing the relation between 4d theories and matrix models. Examples of such bosonic systems include unitary matrix models and gauged matrix quantum mechanics, which deconstruct 5-dimensional supersymmetric gauge theories, and Chern-Simons gauge theories, which deconstruct gauge theories living on branes wrapped over cycles in Calabi-Yau threefolds.
TL;DR: In this article, the expectation values of chiral operators in supersymmetric U(N) gauge theories with matter in the adjoint, fundamental and anti-fundamental representations were solved.
Abstract: We solve for the expectation values of chiral operators in supersymmetric U(N) gauge theories with matter in the adjoint, fundamental and anti-fundamental representations. A simple geometric picture emerges involving a description by a meromorphic one-form on a Riemann surface. The equations of motion are equivalent to a condition on the integrality of periods of this form. The solution indicates that all semiclassical phases with the same number of U(1) factors are continuously connected.
TL;DR: In this article, the effect of gauge and fermion fields propagating in the bulk in the presence of gauge brane kinetic terms compatible with gauge coupling unification is studied, and the authors present ways of obtaining a consistent description of experimental data, while allowing values of the first Kaluza Klein mode masses of the order of a few TeV.
Abstract: Warped extra dimensions allow a novel way of solving the hierarchy problem, with all fundamental mass parameters of the theory naturally of the order of the Planck scale. The observable value of the Higgs vacuum expectation value is red-shifted, due to the localization of the Higgs field in the extra dimension. It has been recently observed that, when the gauge fields propagate in the bulk, unification of the gauge couplings may be achieved. Moreover, the propagation of fermions in the bulk allows for a simple solution to potentially dangerous proton decay problems. However, bulk gauge fields and fermions pose a phenomenological challenge, since they tend to induce large corrections to the precision electroweak observables. In this article, we study in detail the effect of gauge and fermion fields propagating in the bulk in the presence of gauge brane kinetic terms compatible with gauge coupling unification, and we present ways of obtaining a consistent description of experimental data, while allowing values of the first Kaluza Klein mode masses of the order of a few TeV.
TL;DR: In this article, the action of N = 1 super-Yang-Mills theory with chiral and antichiral superfields has been studied on the non-commutative superspace.
TL;DR: In this paper, the authors define the notion of spin network states for non-compact groups and show how the delicate issue of taking the quotient of a space by noncompact group can be addressed in terms of algebraic geometry.
Abstract: Spin networks are a natural generalization of Wilson loop functionals. They have been extensively studied in the case where the gauge group is compact and it has been shown that they naturally form a basis of gauge invariant observables. Physically the restriction to compact gauge groups is enough for the study of Yang–Mills theories, however it is well known that noncompact groups naturally arise as internal gauge groups for Lorentzian gravity models. In this context, a proper construction of gauge invariant observables is needed. The purpose of the present work is to define the notion of spin network states for noncompact groups. We first build, by a careful gauge fixing procedure, a natural measure and a Hilbert space structure on the space of gauge invariant graph connections. Spin networks are then defined as generalized eigenvectors of a complete set of hermitic commuting operators. We show how the delicate issue of taking the quotient of a space by noncompact groups can be address in term of algebraic geometry. We finally construct the full Hilbert space containing all spin network states. Having in mind applications to gravity, we illustrate our results for the groups SL(2,R) and SL(2,C).
TL;DR: In this paper, the anomalous dimension of the local composite operator A 2 is analyzed in pure Yang-Mills theory in the Landau gauge within the algebraic renormalization.
TL;DR: In this article, the second-order field equations and actions for higher spin tensor gauge fields were constructed for general higher spin boson fields, and first-order ones for fermions, which are non-local but which become local on gauge fixing or on introducing auxiliary fields.
Abstract: Higher spin tensor gauge fields have natural gauge-invariant field equations written in terms of generalised curvatures, but these are typically of higher than second order in derivatives. We construct geometric second order field equations and actions for general higher spin boson fields, and first order ones for fermions, which are non-local but which become local on gauge-fixing, or on introducing auxiliary fields. This generalises the results of Francia and Sagnotti to all representations of the Lorentz group.
TL;DR: In this paper, it was shown that non-anti-commutative deformation in four dimensions with N = 1/2 supersymmetry is renormalizable to all orders in perturbation theory.
Abstract: Non(anti)commutative gauge theories are supersymmetric Yang-Mills and matter system defined on a deformed superspace whose coordinates obey non(anti)commutative algebra. We prove that these theories in four dimensions with N=1/2 supersymmetry are renormalizable to all orders in perturbation theory. Our proof is based on operator analysis and symmetry arguments. In a case when the Grassman-even coordinates are commutative, deformation induced by non(anti)commutativity of the Grassman-odd coordinates contains operators of dimension-four or higher. Nevertheless, they do not lead to power divergences in a loop diagram because of absence of operators Hermitian-conjugate to them. In a case when the Grassman-even coordinates are noncommutative, the ultraviolet-infrared mixing makes the theory renormalizable by the planar diagrams, and the deformed operators are not renormalized at all. We also elucidate relation at quantum level between non(anti)commutative deformation and N=1/2 supersymmetry. We point out that the star product structure dictates a specific relation for renormalization among the deformed operators.
TL;DR: In this paper, a supersymmetric U(N) gauge theory with matter fields in the adjoint, fundamental and anti-fundamental representations was considered and the equivalence of the gauge theory and the matrix model was shown.
Abstract: We consider a supersymmetric U(N) gauge theory with matter fields in the adjoint, fundamental and anti-fundamental representations. As in the framework which was put forward by Dijkgraaf and Vafa, this theory can be described by a matrix model. We analyze this theory along the lines of (F. Cachazo, M. Douglas, N.S. and E. Witten, ``Chiral Rings and Anomalies in Supersymmetric Gauge Theory'' [26]) and show the equivalence of the gauge theory and the matrix model. In particular, the anomaly equations in the gauge theory are identified with the loop equations in the matrix model.
TL;DR: In this paper, the authors review some of the efforts aimed at extending the gauge/gravity correspondence to nonconformal supersymmetric gauge theories in four dimensions, and explore in particular which gauge theory information can be extracted from corresponding supergravity solutions, and what the remaining open problems are.
Abstract: We review in a pedagogical manner some of the efforts aimed at extending the gauge/gravity correspondence to nonconformal supersymmetric gauge theories in four dimensions. After giving a general overview, we discuss in detail two specific examples: fractional D-branes on orbifolds and D-branes wrapped on supersymmetric cycles of Calabi–Yau spaces. We explore in particular which gauge theory information can be extracted from the corresponding supergravity solutions, and what the remaining open problems are. We also briefly explain the connection between these and other approaches, such as fractional branes on conifolds, branes suspended between branes, M5-branes on Riemann surfaces and M-theory on G2-holonomy manifolds, and discuss the role played by geometric transitions in all that.
01 Feb 2003
TL;DR: In this paper, it was shown that BPS correlation functions in the N = 2 supersymmetric gauge theories are described by an auxiliary two dimensional conformal field theory, which coincides with the tau-function of the Toda lattice hierarchy.
Abstract: We present new evidence for the conjecture that BPS correlation functions in the N = 2 supersymmetric gauge theories are described by an auxiliary two dimensional conformal field theory We study deformations of the N = 2 supersymmetric gauge theory by all gauge-invariant chiral operators We calculate the partition function of the N = 2 theory on R 4 with appropriately twisted boundary conditions For the U(1) theory with instantons (either noncommutative, or D-instantons, depending on the construction) the partition function has a representation in terms of the theory of free fermions on a sphere, and coincides with the tau-function of the Toda lattice hierarchy Using this result we prove to all orders in string loop expansion that the effective prepotential (for U(1) with all chiral couplings included) is given by the free energy of the topological string on CP 1 ~
TL;DR: In this paper, the relation between supersymmetric gauge theories and matrix models beyond the planar limit has been investigated by summing genus one matrix model diagrams, which give the leading $1/N^2$ corrections in the large $N$ limit of the matrix model.
Abstract: We provide evidence of the relation between supersymmetric gauge theories and matrix models beyond the planar limit. We compute gravitational $R^2$ couplings in gauge theories perturbatively, by summing genus one matrix model diagrams. These diagrams give the leading $1/N^2$ corrections in the large $N$ limit of the matrix model and can be related to twist field correlators in a collective conformal field theory. In the case of softly broken $SU(N)\ \cN=2$ super Yang-Mills theories, we find that these exact solutions of the matrix models agree with results obtained by topological field theory methods.
TL;DR: By applying mirror symmetry to D-branes in a Calabi-Yau geometry, this paper shed light on a G2 flop in M-theory relevant for large N dualities in = 1 supersymmetric gauge theories.
Abstract: By applying mirror symmetry to D-branes in a Calabi-Yau geometry we shed light on a G2 flop in M-theory relevant for large N dualities in = 1 supersymmetric gauge theories. Furthermore, we derive superpotential for M-theory on corresponding G2 manifolds for all A-D-E cases. This provides an effective method for geometric engineering of = 1 gauge theories for which mirror symmetry gives exact information about vacuum geometry. We also find a number of interesting dual descriptions.
TL;DR: Gauge unification in a five dimensional supersymmetric SO(10) model compactified on an orbifold S1/(Z2? Z2') is studied in this paper.
Abstract: Gauge unification in a five dimensional supersymmetric SO(10) model compactified on an orbifold S1/(Z2 ? Z2') is studied. One orbifolding reduces N = 2 supersymmetry to N = 1, and the other breaks SO(10) to the Pati-Salam gauge group SU(4)C ? SU(2)L ? SU(2)R. Further breaking to the standard model gauge group is made through the Higgs mechanism on one of the branes. The differences of the three gauge couplings run logarithmically even in five dimensions and we can keep the predictability for unification as in four dimensional gauge theories. We obtain an excellent prediction for gauge coupling unification with a cutoff scale M* ~ 3 ? 1017 GeV and a compactification scale Mc ~ 1.5 ? 1014 GeV. Finally, although proton decay due to dimension 5 operators may be completely eliminated, the proton decay rate in these models is sensitive to the placement of matter multiplets in the 5th dimension, as well as to the unknown physics above the cutoff scale.
TL;DR: P-term inflation is a version of hybrid inflation which naturally appears in some brane inflation models It was introduced in the framework of N = 2 supersymmetric gauge theory where superconformal SU(2,2|2) symmetry is broken down to N = 1 supersymmetry by the vev of the auxiliary triplet field as discussed by the authors.
Abstract: P-term inflation is a version of hybrid inflation which naturally appears in some brane inflation models It was introduced in the framework of N = 2 supersymmetric gauge theory where superconformal SU(2,2|2) symmetry is broken down to N = 2 supersymmetry by the vev of the auxiliary triplet field Depending on the direction of this vev, one can get either D-term inflation or F-term inflation with a particular relation between Yukawa and gauge coupling, or a mix of these models We show that F and D models, before coupling to gravity is included, are related by a change of variables Coupling of this model to N = 1 supergravity breaks this symmetry and introduces a class of P-term models interpolating between D-term and F-term inflation The difference between these models is determined by the direction of the vector , which depends on the fluxes in the underlying D3/D7 model of brane inflation We discuss cosmological consequences of various versions of P-term inflation