Publications (20)0 Total impact
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Article: Large rank Wilson loops in N=2 superconformal QCD at strong coupling
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ABSTRACT: We compute the expectation values of circular Wilson loops in large representations at strong coupling, in the large-N limit of the N=2 superconformal theory with SU(N) gauge group and 2N hypermultiplets. Employing Pestun's matrix integral, we focus attention on symmetric and antisymmetric representations with ranks of order N. We find that large rank antisymmetric loops are independent of the coupling at strong 't Hooft coupling while symmetric Wilson loops grow exponentially with it. Symmetric loops display a non-analyticity as a function of the rank, characterized by the splitting of a single matrix model eigenvalue from the continuum, bearing close resemblance to Bose-Einstein condensation in an ideal gas. We discuss implications of these for a putative large-N string dual. The method of calculation we adopt makes explicit the connection to Fermi and Bose gas descriptions and also suggests a tantalizing connection of the above system to a multichannel Kondo model.12/2011; -
Article: Weak coupling large-N transitions at finite baryon density
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ABSTRACT: We study thermodynamics of free SU(N) gauge theory with a large number of colours and flavours on a three-sphere, in the presence of a baryon number chemical potential. Reducing the system to a holomorphic large-N matrix integral, paying specific attention to theories with scalar flavours (squarks), we identify novel third-order deconfining phase transitions as a function of the chemical potential. These transitions in the complex large-N saddle point configurations are interpreted as "melting" of baryons into (s)quarks. They are triggered by the exponentially large (~ exp(N)) degeneracy of light baryon-like states, which include ordinary baryons, adjoint-baryons and baryons made from different spherical harmonics of flavour fields on the three-sphere. The phase diagram of theories with scalar flavours terminates at a phase boundary where baryon number diverges, representing the onset of Bose condensation of squarks.10/2011; -
Article: N=4 SYM on S^3 with Near Critical Chemical Potentials
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ABSTRACT: We study the N = 4 theory at weak coupling, on a three sphere in the grand canonical ensemble with R symmetry chemical potentials. We focus attention on near critical values for the chemical potentials, above which the classical theory has no ground state. By computing a one loop effective potential for the light degrees of freedom in this regime, we show the existence of flat directions of complex dimension N, 2N and 3N for one, two and three critical chemical potentials respectively; these correspond to one half, one quarter and one-eighth BPS states becoming light respectively at the critical values. At small finite temperature we show that the chemical potentials can be continued beyond their classical limiting values to yield a deconfined metastable phase with lifetime diverging in the large N limit. Our low temperaure analysis complements the high temperature metastability found by Yamada and Yaffe. The resulting phase diagram at weak coupling bears a striking resemblance to the strong coupling phase diagram for charged AdS black holes. Our analysis also reveals subtle qualitative differences between the two regimes.04/2008; -
Article: Thermal N= 4 supersymmetric Yang-Mills theory as a 2D Coulomb gas
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ABSTRACT: We consider N=4 supersymmetric Yang-Mills theory with SU(N) gauge group at large N and at finite temperature on a spatial S3. We show that, at finite weak ’t Hooft coupling, a sector of the theory is naturally described as a two-dimensional Coulomb gas of complex eigenvalues, ΦJ+iA0, valued on the cylinder. In the low temperature confined phase the eigenvalues condense onto a strip encircling the cylinder, while the high temperature deconfined phase is characterized by an ellipsoidal droplet of eigenvalues.Phys. Rev. D. 07/2007; 76(2). -
Article: Topology change and new phases in thermal N= 4 SYM theory
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ABSTRACT: We characterise the ground state of weakly coupled N = 4 super Yang-Mills theory on S 1 × S 3 by a joint eigenvalue distribution for seven scalar fields, {A 0 , Φ J }. We show that at temperatures below the Hagedorn/'deconfinement' transition the distribution is S 1 × S 5 . At high temperatures T ≫ 1/R S 3 , the eigenvalues form an ellipsoid with topology S 6 . We show how the deconfinement transition realises the topology change S 1 × S 5 → S 6 . Furthermore, we find compelling evidence that when the temperature is increased to T = 1/(√ λR S 3) the phase with S 6 topology changes continuously to one with S 5 topology in a new second order quantum phase transition, separating the weak and strong coupling regimes at high temperature.04/2007; -
Article: Topology change in commuting saddles of thermal N=4 SYM theory
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ABSTRACT: We study the large N saddle points of weakly coupled N=4 super Yang-Mills theory on S^1 x S^3 that are described by a commuting matrix model for the seven scalar fields {A_0, \Phi_J}. We show that at temperatures below the Hagedorn/`deconfinement' transition the joint eigenvalue distribution is S^1 x S^5. At high temperatures T >> 1/R_{S^3}, the eigenvalues form an ellipsoid with topology S^6. We show how the deconfinement transition realises the topology change S^1 x S^5 --> S^6. Furthermore, we find compelling evidence that when the temperature is increased to T = 1/(\sqrt\lambda R_{S^3}) the saddle with S^6 topology changes continuously to one with S^5 topology in a new second order quantum phase transition occurring in these saddles.03/2007; -
Article: Thermal N = 4 SYM theory as a 2D Coulomb gas
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ABSTRACT: We consider N = 4 supersymmetric Yang-Mills theory with SU(N) gauge group at large N and at finite temperature on a spatial S^3. We show that, at finite weak 't Hooft coupling, the theory is naturally described as a two dimensional Coulomb gas of complex eigenvalues of the Polyakov-Maldacena loop, valued on the cylinder. In the low temperature confined phase the eigenvalues condense onto a strip encircling the cylinder, while the high temperature deconfined phase is characterised by an ellipsoidal droplet of eigenvalues.11/2006; -
Article: Instabilities of the Small Black Hole: a view from N=4 SYM
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ABSTRACT: We compute a one-loop effective action for the constant modes of the scalars and the Polyakov loop matrix of N=4 SYM on S^3 at finite temperature and weak 't Hooft coupling. Above a critical temperature, the effective potential develops new unstable directions accompanied by new saddle points which only preserve an SO(5) subgroup of the SO(6) global R-symmetry. We identify this phenomenon as the weak coupling version of the well known Gregory-Laflamme localization instability in the gravity dual of the strongly coupled field theory: The small AdS_5 black hole when viewed as a ten dimensional, asymptotically AdS_5 X S^5 solution smeared on the S^5 is unstable to localization on S^5. Our effective potential, in a specific Lorentzian continuation, can provide a qualitative holographic description of the decay of the "topological black hole'' into the AdS bubble of nothing. Comment: 39 pages, 6 figures, uses JHEP3.cls, references added07/2006; -
Article: Higher rank Wilson loops from a matrix model
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ABSTRACT: We compute the circular Wilson loop of N=4 SYM theory at large N in the rank k symmetric and antisymmetric tensor representations. Using a quadratic Hermitian matrix model we obtain expressions for all values of the 't Hooft coupling. At large and small couplings we give explicit formulae and reproduce supergravity results from both D3 and D5 branes within a systematic framework.05/2006; -
Article: Multiply wound Polyakov loops at strong coupling
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ABSTRACT: We study the expectation value of a Polyakov-Maldacena loop that wraps the thermal circle k times in strongly coupled N=4 super Yang-Mills theory. This is achieved by considering probe D3 and D5 brane embeddings in the dual black hole geometry. In contrast to multiply wound spatial Wilson loops, nontrivial dependence on k is captured through D5 branes. We find N^{-2/3} corrections, reminiscent of the scaling behaviour near a Gross-Witten transition.04/2006; -
Article: AdS black holes and thermal Yang-Mills correlators
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ABSTRACT: We study the real time correlators of scalar glueball operators for Yang-Mills theory at finite temperature in flat space. The analytic structure of the frequency space propagator in perturbative field theory is seen to be qualitatively different to the strong coupling results that may be obtained from perturbations about AdS black hole spacetimes: we find branch cuts rather than poles. This difference appears to persist away from the strict zero and infinite coupling limits, possibly suggesting a phase transition in large N thermal N = 4 SYM theory as a function of the 't Hooft coupling.08/2005; -
Article: The O(N) model on a squashed S^3 and the Klebanov-Polyakov correspondence
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ABSTRACT: We solve the O(N) vector model at large N on a squashed three-sphere with a conformal mass term. Using the Klebanov-Polyakov version of the AdS_4/CFT_3 correspondence we match various aspects of the strongly coupled theory with the physics of the bulk AdS Taub-NUT and AdS Taub-Bolt geometries. Remarkably, we find that the field theory reproduces the behaviour of the bulk free energy as a function of the squashing parameter. The O(N) model is realised in a symmetric phase for all finite values of the coupling and squashing parameter, including when the boundary scalar curvature is negative.03/2005; -
Article: An N=1 duality cascade from a deformation of N=4 SUSY Yang-Mills
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ABSTRACT: We study relevant deformations of an N=1 superconformal theory which is an exactly marginal deformation of U(N) N=4 SUSY Yang-Mills. The resulting theory has a classical Higgs branch that is a complex deformation of the orbifold C^3/Z_n x Z_n that is a non-compact Calabi-Yau space with isolated conifold singularities. At these singular points in moduli space the theory exhibits a duality cascade and flows to a confining theory with a mass gap. By exactly solving the corresponding holomorphic matrix model we compute the exact quantum superpotential generated at the end of the duality cascade and calculate precisely how quantum effects deform the classical moduli space by replacing the conifold singularities with three-cycles of finite size. Locally the structure is that of the deformed conifold, but the global geometry is different. This desingularized quantum deformed geometry is the moduli space of probe D3-branes at the end of a duality cascade realized on the worldvolume of (fractional) D3-branes placed at the isolated conifold singularities in the deformation of the orbifold C^3/Z_n x Z_n with discrete torsion.07/2004; -
Article: S-duality of the Leigh-Strassler Deformation via Matrix Models
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ABSTRACT: We investigate an exactly marginal N=1 supersymmetric deformation of SU(N) N=4 supersymmetric Yang-Mills theory discovered by Leigh and Strassler. We use a matrix model to compute the exact superpotential for a further massive deformation of the U(N) Leigh-Strassler theory. We then show how the exact superpotential and eigenvalue spectrum for the SU(N) theory follows by a process of integrating-in. We find that different vacua are related by an action of the SL(2,Z) modular group on the bare couplings of the theory extending the action of electric-magnetic duality away from the N=4 theory. We perform non-trivial tests of the matrix model results against semiclassical field theory analysis. We also show that there are interesting points in parameter space where condensates can diverge and vacua disappear. Based on the matrix model results, we propose an exact elliptic superpotential to describe the theory compactified on a circle of finite radius. Comment: 33 pages, 2 figures, uses JHEP.cls; minus sign typo corrected and 1 reference added, submitted to JHEP10/2002; -
Article: Massive Vacua of N=1* Theory and S-duality from Matrix Models
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ABSTRACT: In this note we show how Dijkgraaf and Vafa's hypothesis relating the exact superpotential of an N=1 theory to a matrix model can be used to describe all the massive vacua of the N=1*, or mass deformed N=4, theory including the Higgs vacuum. The matrix model computation of the superpotential for each massive vacuum independently yields a modular function of the associated effective coupling in that vacuum which agrees with previously derived results up to a vacuum-independent additive constant. The results in the different massive vacua can be related by the action of SL(2,Z) on the N=4 coupling, thus providing evidence for modular invariance of the underlying N=4 theory.09/2002; -
Article: Exact Superpotentials from Matrix Models
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ABSTRACT: Dijkgraaf and Vafa (DV) have conjectured that the exact superpotential for a large class of N=1 SUSY gauge theories can be extracted from the planar limit of a certain holomorphic matrix integral. We test their proposal against existing knowledge for a family of deformations of N=4 SUSY Yang-Mills theory involving an arbitrary polynomial superpotential for one of the three adjoint chiral superfields. Specifically, we compare the DV prediction for these models with earlier results based on the connection between SUSY gauge theories and integrable systems. We find complete agreement between the two approaches. In particular we show how the DV proposal allows the extraction of the exact eigenvalues of the adjoint scalar in the confining vacuum and hence computes all related condensates of the finite-N gauge theory. We extend these results to include Leigh-Strassler deformations of the N=4 theory. Comment: 28 pages, 1 figure, latex with JHEP.cls, replaced with typos corrected and one clarifying comment09/2002; -
Article: World-sheet Instantons via the Myers Effect and N=1^* Quiver Superpotentials
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ABSTRACT: In this note we explore the stringy interpretation of non-perturbative effects in N=1^* deformations of the A_{k-1} quiver models. For certain types of deformations we argue that the massive vacua are described by Nk fractional D3-branes at the orbifold polarizing into k concentric 5-brane spheres each carrying fractional brane charge. The polarization of the D3-branes induces a polarization of D-instantons into string world-sheets wrapped on the Myers spheres. We show that the superpotentials in these models are indeed generated by these world-sheet instantons. We point out that for certain parameter values the condensates yield the exact superpotential for a relevant deformation of the Klebanov-Witten conifold theory.06/2002; -
Article: New modular invariance in the N=1* theory, operator mixings and supergravity singularities
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ABSTRACT: We discuss the mass-deformed N=4 SU(N) supersymmetric Yang-Mills theory (also known as the N=1* theory). We analyze how the correlation functions of this theory transform under S-duality, and which correlation functions depend holomorphically on the complexified gauge coupling \tau. We provide exact modular-covariant expressions for the vacuum expectation values of chiral operators in the massive vacua of the N=1* theory. We exhibit a novel modular symmetry of the chiral sector of the theory in each vacuum, which acts on the coupling ${\tilde \tau}= (p\tau+k)/q$, where p, k and q are integers which label the different vacua. In the strong coupling limit, we compare our results to the results of Polchinski and Strassler in the string theory dual of this theory, and find non-trivial agreement after operator mixings are taken into account. In particular we find that their results are consistent with the predicted modular symmetry in ${\tilde \tau}$. Our results imply that certain singularities found in solutions to five dimensional gauged supergravity should not be resolvable in string theory, since there are no field theory vacua with corresponding vacuum expectation values in the large N limit. Comment: 28 pages, harvmac06/2000; -
Article: Softly-Broken {\cal N} = 4 Supersymmetry in the Large-N Limit
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ABSTRACT: We calculate the exact values of the holomorphic observables of {\cal N}=4 supersymmetric SU(N) Yang-Mills theory deformed by mass terms which preserve {\cal N}=1 SUSY. These include the chiral condensates in each massive vacuum of the theory as well as the central charge which determines the tension of BPS saturated domain walls interpolating between these vacua. Several unexpected features emerge in the large-N limit, including anomalous modular properties under an SL(2,Z) duality group which acts on a complexification of the 't Hooft coupling \lambda=g^{2}N/4\pi. We discuss our results in the context of the AdS/CFT correspondence.01/2000; -
Article: An exact elliptic superpotential for N=1∗ deformations of finite N=2 gauge theories
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ABSTRACT: We study relevant deformations of the superconformal theory on the world-volume of N D3-branes at an Ak−1 singularity. In particular, we determine the vacuum structure of the mass-deformed theory with supersymmetry and show how the different vacua are permuted by an extended duality symmetry. We then obtain exact, modular covariant formulae (for all k, N and arbitrary gauge couplings) for the holomorphic observables in the massive vacua in two different ways: by lifting to M-theory, and by compactification to three dimensions and subsequent use of mirror symmetry. In the latter case, we find an exact superpotential for the model which coincides with a certain combination of the quadratic Hamiltonians of the spin generalization of the elliptic Calogero–Moser integrable system.Nuclear Physics B.
Top co-authors
Institutions
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2007
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University of California, Santa Barbara
Santa Barbara, CA, USA
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2006–2007
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Swansea University
- Department of Physics
Swansea, WLS, United Kingdom
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