arXiv subjects

Sean A. Hartnoll

Publications and source records attributed to Sean A. Hartnoll.

At least 109 records · Page 6Linked to original sources

arXiv2008

Impure AdS/CFT

We study momentum relaxation due to dilute, weak impurities in a strongly coupled CFT, a truncation of the M2 brane theory. Using the AdS/CFT correspondence, we compute the relaxation time scale as a function of the background magnetic field B and charge density ρ. The theory admits two different types of impurities. We find that for magnetic impurities, momentum relaxation due to the impurity is suppressed by a background B or ρ. For electric impurities, due to an underlying instability in the theory towards an ordered phase, the inverse relaxation time scale increases dramatically near \sqrt{B^2 + ρ^2/σ^2_0} \sim 21 T^2. We compute the Nernst response for the impure theory, and comment on similarities with recent measurements in superconductors.

hep-th↗

arXiv2007

Strings on conifolds from strong coupling dynamics: quantitative results

Three quantitative features of string theory on AdS_5 x X_5, for any (quasi)regular Sasaki-Einstein X_5, are recovered exactly from an expansion of field theory at strong coupling around configurations in the moduli space of vacua. These configurations can be thought of as a generalized matrix model of (local) commuting matrices. First, we reproduce the spectrum of scalar Kaluza-Klein modes on X_5. Secondly, we recover the precise spectrum of BMN string states, including a nontrivial dependence on the volume of X_5. Finally, we show how the radial direction in global AdS_5 emerges universally in these theories by exhibiting states dual to AdS giant gravitons.

hep-th↗

arXiv2007

Hall conductivity from dyonic black holes

A class of strongly interacting 2+1 dimensional conformal field theories in a transverse magnetic field can be studied using the AdS/CFT duality. We compute zero momentum hydrodynamic response functions of maximally supersymmetric 2+1 dimensional SU(N) Yang-Mills theory at the conformal fixed point, in the large N limit. With background magnetic field B and electric charge density rho, the Hall conductivity is found to be rho/B. The result, anticipated on kinematic grounds in field theory, is obtained from perturbations of a four dimensional AdS black hole with both electric and magnetic charges.

hep-th↗

arXiv2007

Ohm's Law at strong coupling: S duality and the cyclotron resonance

We calculate the electrical and thermal conductivities and the thermoelectric coefficient of a class of strongly interacting 2+1 dimensional conformal field theories with anti-de Sitter space duals. We obtain these transport coefficients as a function of charge density, background magnetic field, temperature and frequency. We show that the thermal conductivity and thermoelectric coefficient are determined by the electrical conductivity alone. At small frequency, in the hydrodynamic limit, we are able to provide a number of analytic formulae for the electrical conductivity. A dominant feature of the conductivity is the presence of a cyclotron pole. We show how bulk electromagnetic duality acts on the transport coefficients.

hep-th↗

arXiv2007

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

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, Φ_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/(\sqrtλR_{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.

hep-th↗

arXiv2007

Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes

We present a general hydrodynamic theory of transport in the vicinity of superfluid-insulator transitions in two spatial dimensions described by "Lorentz"-invariant quantum critical points. We allow for a weak impurity scattering rate, a magnetic field B, and a deviation in the density, ρ, from that of the insulator. We show that the frequency-dependent thermal and electric linear response functions, including the Nernst coefficient, are fully determined by a single transport coefficient (a universal electrical conductivity), the impurity scattering rate, and a few thermodynamic state variables. With reasonable estimates for the parameters, our results predict a magnetic field and temperature dependence of the Nernst signal which resembles measurements in the cuprates, including the overall magnitude. Our theory predicts a "hydrodynamic cyclotron mode" which could be observable in ultrapure samples. We also present exact results for the zero frequency transport co-efficients of a supersymmetric conformal field theory (CFT), which is solvable by the AdS/CFT correspondence. This correspondence maps the ρand B perturbations of the 2+1 dimensional CFT to electric and magnetic charges of a black hole in the 3+1 dimensional anti-de Sitter space. These exact results are found to be in full agreement with the general predictions of our hydrodynamic analysis in the appropriate limiting regime. The mapping of the hydrodynamic and AdS/CFT results under particle-vortex duality is also described.

cond-mat.str-el↗

arXiv2007

A phase transition in commuting Gaussian multi-matrix models

We analyze in detail a second order phase transition that occurs in large N Gaussian multi-matrix models in which the matrices are constrained to be commuting. The phase transition occurs as the relative masses of the matrices are varied, assuming that there are at least four matrices in the lowest mass level. We also discuss the phase structure of weakly coupled large N 3+1 dimensional gauge theories compactified on a three-sphere of radius R. We argue that these theories are well described at high temperatures (T >> 1/R) by a Gaussian multi-matrix model, and that they do not exhibit any phase transitions between the deconfinement scale (T ~ 1/R) and the scale where perturbation theory breaks down (T ~ 1 / λR, where λis the 't Hooft coupling).

hep-th↗

arXiv2006

Anyonic strings and membranes in AdS space and dual Aharonov-Bohm effects

It is observed that strings in AdS_5 x S^5 and membranes in AdS_7 x S^4 exhibit long range phase interactions. Two well separated membranes dragged around one another in AdS acquire phases of 2π/N. The same phases are acquired by a well separated F and D string dragged around one another. The phases are shown to correspond to both the standard and a novel type of Aharonov-Bohm effect in the dual field theory.

hep-th↗

arXiv2006

Einstein-Maxwell gravitational instantons and five dimensional solitonic strings

We study various aspects of four dimensional Einstein-Maxwell multicentred gravitational instantons. These are half-BPS Riemannian backgrounds of minimal N=2 supergravity, asymptotic to R^4, R^3 x S^1 or AdS_2 x S^2. Unlike for the Gibbons-Hawking solutions, the topology is not restricted by boundary conditions. We discuss the classical metric on the instanton moduli space. One class of these solutions may be lifted to causal and regular multi `solitonic strings', without horizons, of 4+1 dimensional N=2 supergravity, carrying null momentum.

hep-th↗

arXiv2006

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

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.

hep-th↗

arXiv2006

Two universal results for Wilson loops at strong coupling

We present results for Wilson loops in strongly coupled gauge theories. The loops may be taken around an arbitrarily shaped contour and in any field theory with a dual IIB geometry of the form M x S^5. No assumptions about supersymmetry are made. The first result uses D5 branes to show how the loop in any antisymmetric representation is computed in terms of the loop in the fundamental representation. The second result uses D3 branes to observe that each loop defines a rich sequence of operators associated with minimal surfaces in S^5. The action of these configurations are all computable. Both results have features suggesting a connection with integrability.

hep-th↗

arXiv2006

Higher rank Wilson loops from a matrix model

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.

hep-th↗

arXiv2006

Multiply wound Polyakov loops at strong coupling

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.

hep-th↗

arXiv2005

AdS black holes and thermal Yang-Mills correlators

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.

hep-th↗

arXiv2005

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

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.

hep-th↗

arXiv2005

Properties of some five dimensional Einstein metrics

The volumes, spectra and geodesics of a recently constructed infinite family of five-dimensional inhomogeneous Einstein metrics on the two $S^3$ bundles over $S^2$ are examined. The metrics are in general of cohomogeneity one but they contain the infinite family of homogeneous metrics $T^{p,1}$. The geodesic flow is shown to be completely integrable, in fact both the Hamilton-Jacobi and the Laplace equation separate. As an application of these results, we compute the zeta function of the Laplace operator on $T^{p,1}$ for large $p$. We discuss the spectrum of the Lichnerowicz operator on symmetric transverse tracefree second rank tensor fields, with application to the stability of Freund-Rubin compactifications and generalised black holes.

hep-th↗

arXiv2004

Spacetime foam in twistor string theory

We show how a Kahler spacetime foam in four dimensional conformal (super)gravity may be mapped to twistor spaces carrying the D1 brane charge of the B model topological string theory. The spacetime foam is obtained by blowing up an arbitrary number of points in $\C^2$ and can be interpreted as a sum over gravitational instantons. Some twistor spaces for blowups of $\C^2$ are known explicitly. In these cases we write down a meromorphic volume form and suggest a relation to a holomorphic superform on a corresponding super Calabi-Yau manifold.

hep-th↗

arXiv2004

On the stability of naked singularities

We study the linearised stability of the nakedly singular negative mass Schwarzschild solution against gravitational perturbations. There is a one parameter family of possible boundary conditions at the singularity. We give a precise criterion for stability depending on the boundary condition. We show that one particular boundary condition is physically preferred and show that the spacetime is stable with this boundary condition.

hep-th↗