Sean A. Hartnoll

Publications (11)0 Total impact

• Article: Thermal N= 4 supersymmetric Yang-Mills theory as a 2D Coulomb gas

  Sean A. Hartnoll, S. Prem Kumar
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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).
• Source

  Available from: cern.ch

  Article: Topology change and new phases in thermal N= 4 SYM theory

  Umut Gürsoy, Sean A Hartnoll, Timothy J Hollowood, S Prem Kumar
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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;
• Source

  Available from: ArXiv

  Article: Topology change in commuting saddles of thermal N=4 SYM theory

  Umut Gursoy, Sean A. Hartnoll, Timothy J. Hollowood, S. Prem Kumar
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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;
• Source

  Available from: arxiv.org

  Article: Thermal N = 4 SYM theory as a 2D Coulomb gas

  Sean A. Hartnoll, S. Prem Kumar
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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;
• Source

  Available from: arxiv.org

  Article: Higher rank Wilson loops from a matrix model

  Sean A. Hartnoll, S. Prem Kumar
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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;
• Source

  Available from: arxiv.org

  Article: Multiply wound Polyakov loops at strong coupling

  Sean A. Hartnoll, S. Prem Kumar
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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;
• Source

  Available from: arxiv.org

  Article: AdS black holes and thermal Yang-Mills correlators

  Sean A. Hartnoll, S. Prem Kumar
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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;
• Source

  Available from: arxiv.org

  Article: The O(N) model on a squashed S^3 and the Klebanov-Polyakov correspondence

  Sean A. Hartnoll, S. Prem Kumar
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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;
• Source

  Available from: arxiv.org

  Article: Deforming baryons into confining strings

  Sean A. Hartnoll, Ruben Portugues
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  ABSTRACT: We find explicit probe D3-brane solutions in the infrared of the Maldacena-Nunez background. The solutions describe deformed baryon vertices: q external quarks are separated in spacetime from the remaining N-q. As the separation is taken to infinity we recover known solutions describing infinite confining strings in ${\mathcal{N}}=1$ gauge theory. We present results for the mass of finite confining strings as a function of length. We also find probe D2-brane solutions in a confining type IIA geometry, the reduction of a G_2 holonomy M theory background. The relation between these deformed baryons and confining strings is not as straightforward. Comment: 1+13 pages. LaTeX. 3 Figures. Factor of 2N fixed to N for the IIA background. Minor changes to text
  05/2004;
• Source

  Available from: arxiv.org

  Article: The chiral anomaly from M theory

  Umut Gursoy, Sean A. Hartnoll, Ruben Portugues
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  ABSTRACT: We argue that the chiral anomaly of $\Ncal = 1$ super Yang-Mills theory admits a dual description as spontaneous symmetry breaking in M theory on $G_2$ holonomy manifolds. We identify an angle of the $G_2$ background dual to the anomalous $U(1)_R$ current in field theory. This angle is not an isometry of the metric and we therefore develop a theory of ``massive isometry'' to describe fluctuations about such angles. Another example of a massive isometry occurs in the Atiyah-Hitchin metric. Comment: 1 + 44 pages. LaTeX
  11/2003;
• Source

  Available from: cern.ch

  Article: Missing Yang-Mills instantons on ALE spaces

  Sean A. Hartnoll, Ruben Portugues
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  ABSTRACT: Paper withdrawn due to a crucial algebraic error in section 3.
  06/2002;