arXiv subjects

Benjamin Withers

Publications and source records attributed to Benjamin Withers.

54 records · Page 3Linked to original sources

arXiv2014

Moduli dynamics as a predictive tool for thermal maximally supersymmetric Yang-Mills at large N

Maximally supersymmetric (p+1)-dimensional Yang-Mills theory at large N and finite temperature, with possibly compact spatial directions, has a rich phase structure. Strongly coupled phases may have holographic descriptions as black branes in various string duality frames, or there may be no gravity dual. In this paper we provide tools in the gauge theory which give a simple and unified picture of the various strongly coupled phases, and transitions between them. Building on our previous work we consider the effective theory describing the moduli of the gauge theory, which can be computed precisely when it is weakly coupled far out on the Coulomb branch. Whilst for perturbation theory naive extrapolation from weak coupling to strong gives little information, for this moduli theory naive extrapolation from its weakly to its strongly coupled regime appears to encode a surprising amount of information about the various strongly coupled phases. We argue it encodes not only the parametric form of thermodynamic quantities for these strongly coupled phases, but also certain transcendental factors with a geometric origin, and allows one to deduce transitions between the phases. We emphasise it also gives predictions for the behaviour of a large class of local operators in these phases.

hep-th↗

arXiv2014

Holographic Checkerboards

We construct cohomogeneity-three, finite temperature stationary black brane solutions dual to a field theory exhibiting checkerboard order. The checkerboards form a backreacted part of the bulk solution, and are obtained numerically from the coupled Einstein-Maxwell-scalar PDE system. They arise spontaneously and without the inclusion of an explicit lattice. The phase exhibits both charge and global U(1)-current modulation, which are periodic in two spatial directions. The current circulates within each checkerboard plaquette. We explore the competition with striped phases, finding first-order checkerboard to stripe phase transitions. We also detail spatially modulated instabilities of asymptotically AdS black brane backgrounds with neutral scalar profiles, including those with an hyperscaling violating IR geometry at zero temperature.

hep-th↗

arXiv2013

Black holes as bubble nucleation sites

We consider the effect of inhomogeneities on the rate of false vacuum decay. Modelling the inhomogeneity by a black hole, we construct explicit Euclidean instantons which describe the nucleation of a bubble of true vacuum centred on the inhomogeneity. We find that inhomogeneity significantly enhances the nucleation rate over that of the Coleman-de Luccia instanton -- the black hole acts as a nucleation site for the bubble. The effect is larger than previously believed due to the contributions to the action from conical singularities. For a sufficiently low initial mass, the original black hole is replaced by flat space during this process, as viewed by a single causal patch observer. Increasing the initial mass, we find a critical value above which a black hole remnant survives the process. This resulting black hole can have a higher mass than the original black hole, but always has a lower entropy. We compare the process to bubble-to-bubble transitions, where there is a semi-classical Lorentzian description in the WKB approximation.

hep-th↗

arXiv2013

A simple holographic model of momentum relaxation

We consider a holographic model consisting of Einstein-Maxwell theory in (d+1) bulk spacetime dimensions with (d-1) massless scalar fields. Momentum relaxation is realised simply through spatially dependent sources for operators dual to the neutral scalars, which can be engineered so that the bulk stress tensor and resulting black brane geometry are homogeneous and isotropic. We analytically calculate the DC conductivity, which is finite. In the d=3 case, both the black hole geometry and shear-mode current-current correlators are those of a sector of massive gravity.

hep-th↗

arXiv2013

Warm p-soup and near extremal black holes

We consider a model of D-dimensional supergravity coupled to elementary p-branes. We use gravitational arguments to deduce the low energy effective theory of N nearly parallel branes. This is a (p+1)-dimensional scalar field theory, where the scalars represent the positions of the branes in their transverse space. We propose that the same theory in a certain temperature regime describes a `soup' of strongly interacting branes, giving a microscopic description of near extremal black p-branes. We use natural approximations to estimate the energy density of this soup as a function of the physical parameters; N, temperature, brane tension and gravitational coupling. We also characterise the horizon radius, measured in the metric natural to the branes, with the thermal vev of the scalars. For both quantities we find agreement with the corresponding supergravity black brane results. Surprisingly, beyond the physical parameters, we are naturally able to reproduce certain irrational factors such as pi's. We comment on how these ideas may explain why black hole thermodynamics arises in gauge theories with holographic duals at finite temperature.

hep-th↗

arXiv2013

The moduli space of striped black branes

At finite charge density certain holographic models exhibit the spontaneous breaking of translational invariance resulting in an inhomogeneous phase. We follow up on recent numerical work, reporting results for a larger class of cohomogeneity two black branes in AdS, dual to a holographic striped phase. We construct the continuous moduli space of inhomogeneous black branes as a function of the temperature. Minimising the free energy we determine the dominant striped solutions, revealing a growth in the stripe size as the system is cooled. We discuss the thermodynamic properties of this line of solutions.

hep-th↗

arXiv2013

Black branes dual to striped phases

We construct inhomogeneous charged black branes in AdS, holographically dual to a phase at finite chemical potential with spontaneously broken translation invariance in one direction. These are obtained numerically, solving PDEs for the fully backreacted system. Fixing the periodicity scale, we find a second order phase transition to the inhomogeneous phase. We comment on the properties of the state emerging at low temperatures. For some models we demonstrate the existence of a branch of striped solutions but no continuous phase transition.

hep-th↗

arXiv2013

Bosonic Fractionalisation Transitions

At finite density, charge in holographic systems can be sourced either by explicit matter sources in the bulk or by bulk horizons. In this paper we find bosonic solutions of both types, breaking a global U(1) symmetry in the former case and leaving it unbroken in the latter. Using a minimal bottom-up model we exhibit phase transitions between the two cases, under the influence of a relevant operator in the dual field theory. We also embed solutions and transitions of this type in M-theory, where, holding the theory at constant chemical potential, the cohesive phase is connected to a neutral phase of Schrödinger type via a z=2 QCP.

hep-th↗

arXiv2012

Competing orders in M-theory: superfluids, stripes and metamagnetism

We analyse the infinite class of d=3 CFTs dual to skew-whiffed AdS_4 X SE_7 solutions of D=11 supergravity at finite temperature and charge density and in the presence of a magnetic field. We construct black hole solutions corresponding to the unbroken phase, and at zero temperature some of these become dyonic domain walls of an Einstein-Maxwell-pseudo-scalar theory interpolating between AdS_4 in the UV and new families of dyonic AdS_2 X R^2 solutions in the IR. The black holes exhibit both diamagnetic and paramagnetic behaviour. We analyse superfluid and striped instabilities and show that for large enough values of the magnetic field the superfluid instability disappears while the striped instability remains. For larger values of the magnetic field there is also a first-order metamagnetic phase transition and at zero temperature these black hole solutions exhibit hyperscaling violation in the IR with dynamical exponent z=3/2 and θ=-2.

hep-th↗

arXiv2012

Superconducting instabilities of R-charged black branes

We explore superconducting instabilities of black branes in SO(6) gauged supergravity at finite temperature and finite R-charge densities. We compute the critical temperatures for homogeneous neutral and superconducting instabilities in a truncation of 20 scalars and 15 gauge fields as a function of the chemical potentials conjugate to the three U(1) charges in SO(6). We find that despite the imbalance provided by multiple chemical potentials there is always at least one superconducting black brane branch, emerging at a temperature where the normal phase is locally thermodynamically stable. We emphasise that the three-equal charge solution, Reissner-Nordstrom, is subdominant to a thermodynamically unstable black brane at sufficiently low temperatures --- a feature which is hidden in an equal charge truncation.

hep-th↗

arXiv2012

A soliton menagerie in AdS

We explore the behaviour of charged scalar solitons in asymptotically global AdS4 spacetimes. This is motivated in part by attempting to identify under what circumstances such objects can become large relative to the AdS length scale. We demonstrate that such solitons generically do get large and in fact in the planar limit smoothly connect up with the zero temperature limit of planar scalar hair black holes. In particular, for given Lagrangian parameters we encounter multiple branches of solitons: some which are perturbatively connected to the AdS vacuum and surprisingly, some which are not. We explore the phase space of solutions by tuning the charge of the scalar field and changing scalar boundary conditions at AdS asymptopia, finding intriguing critical behaviour as a function of these parameters. We demonstrate these features not only for phenomenologically motivated gravitational Abelian-Higgs models, but also for models that can be consistently embedded into eleven dimensional supergravity.

hep-th↗

arXiv2011

Fermionic probes of local quantum criticality in one dimension

We study the spectral functions of fermionic operators in 1+1 dimensional SU(N) Super Yang-Mills theory with 16 supercharges at finite density using the holographically dual D1-brane geometry. This system exhibits quasi-particle peaks indicating the existence of Fermi points about which excitations have a finite relaxation time, in contrast with the Tomonaga-Luttinger model. The finite width may be attributed to the non-trivial interactions of the probe operators with the background density matrix, modeled holographically as a charged black hole. We show that the fermionic correlators can in fact be deduced from known results for fermion probes of the charged AdS4 black hole background, owing to some remarkable coincidences in supergravity truncations.

hep-th↗

arXiv2010

Inhomogeneous post-inflationary Lambda-CDM cosmology as a moduli space expansion

We model the large scale late time universe as a Lambda-CDM cosmology driven by cosmological constant and perfect dust fluid. Our aim is to find new solutions in the matter and Lambda epoch consistent with inflationary initial conditions, namely that to the far past in the matter era the cosmology tends to a flat FLRW solution. We identify the moduli degrees of freedom that parametrize the flat Lambda-dust FLRW solution and then promote these moduli to slowly varying functions of the spatial coordinates and show how to solve the Einstein equations in a comoving gradient expansion, controlled by the cosmological constant length scale. Our initial conditions ensure that the approximation remains under control to the far past of the matter era, and to the far future of Lambda domination. The solution is fully non-perturbative in the amplitude of the metric deformation, and we explicitly construct it to fourth order in derivatives. A general Lambda-dust universe dominated by Lambda in the future is characterized by a 3-metric and a stress tensor (with positive trace) defined on the future conformal boundary. The new cosmologies with inflationary initial conditions are characterized only by the boundary 3-metric, the stress tensor being locally determined entirely in terms of that metric.

hep-th↗

arXiv2010

A gravity derivation of the Tisza-Landau Model in AdS/CFT

We derive the fully backreacted bulk solution dual to a boundary superfluid with finite supercurrent density in AdS/CFT. The non-linear boundary hydrodynamical description of this solution is shown to be governed by a relativistic version of the Tisza-Landau two-fluid model to non-dissipative order. As previously noted, the phase transition can be both first order and second order, but in the strongly-backreacted regime at low charge q we find that the transition remains second order for all allowed fractions of superfluid density.

hep-th↗

arXiv2010

Late time solutions for inhomogeneous Lambda-CDM cosmology, their characterization and observation

Assuming homogeneous isotropic Lambda-CDM cosmology allows Lambda, spatial curvature and dark matter density to be inferred from large scale structure observations such as supernovae. The purpose of this paper is to extend this to allow observations to measure or constrain inhomogeneity and anisotropy. We obtain the general inhomogeneous anisotropic Lambda-CDM solution which is locally asymptotic to an expanding de Sitter solution as a late time expansion using Starobinsky's method (analogous to the `holographic renormalization' technique in AdS/CFT) together with a resummation of the series. The dark matter is modeled as perfect dust fluid. The terms in the expansion systematically describe inhomogeneous and anisotropic deformations of an expanding FLRW solution, and are given as a spatial derivative expansion in terms of data characterizing the solution - a 3-metric and a perturbation of that 3-metric. Leading terms describe inhomogeneity and anisotropy on the scale set by the cosmological constant, approximately the horizon scale today. Higher terms in the expansion describe shorter scale variations. We compute the luminosity distance-redshift relation and argue that comparison with current and future observation would allow a partial reconstruction of the characterizing data. We also comment on smoothing these solutions noting that geometric flows (such as Ricci flow) applied to the characterizing data provide a canonical averaging method.

gr-qc↗

arXiv2009

Einstein-aether as a quantum effective field theory

The possibility that Lorentz symmetry is violated in gravitational processes is relatively unconstrained by experiment, in stark contrast with the level of accuracy to which Lorentz symmetry has been confirmed in the matter sector. One model of Lorentz violation in the gravitational sector is Einstein-aether theory, in which Lorentz symmetry is broken by giving a vacuum expectation value to a dynamical vector field. In this paper we analyse the effective theory for quantised gravitational and aether perturbations. We show that this theory possesses a controlled effective expansion within dimensional regularisation, that is, for any process there are a finite number of Feynman diagrams which will contribute to a given order of accuracy. We find that there is no log-running of the two-derivative phenomenological parameters, justifying the use of experimental constraints for these parameters obtained over many orders of magnitude in energy scale. Given the stringent experimental bounds on two-derivative Lorentz-violating operators, we estimate the size of matter Lorentz-violation which arises due to loop effects. This amounts to an estimation of the natural size of coefficients for Lorentz-violating dimension-six matter operators, which in turn can be used to obtain a new bound on the two-derivative parameters of this theory.

gr-qc↗

arXiv2008

TeVeS gets caught on caustics

TeVeS uses a dynamical vector field with timelike unit norm constraint to specify a preferred local frame. When matter moves slowly in this frame - the so-called quasi-static regime - Modified Newtonian Dynamics (MoND) results. Theories with such vectors (such as Einstein-aether) are prone to the vector dynamics forming singularities which render their classical evolution problematic. Here we analyse the dynamics of the vector in TeVeS in various situations. We find that, quite generically, the vector field develops caustic singularities on time scales of order the gravitational in-fall time. Having shown singularity formation is generic with or without matter, Bekenstein's original formulation of TeVeS appears dynamically problematic. We argue that by modifying the vector field kinetic terms to the more general form used by Einstein-Aether this problem may be avoided.

gr-qc↗

arXiv2008

Holographic renormalization for coincident Dp-branes

We consider holographic renormalization for the decoupling limit of coincident Dp-branes. We truncate the theory to the supergravity sector which is homogeneous on the (8-p)-sphere and carries only RR electric (p+2)-flux, leaving a graviton and two scalar degrees of freedom associated to the dilaton and the sphere radius. We non-linearly construct the asymptotic graviton and dilaton deformations - the analog of the Graham-Fefferman expansion for AdS/CFT - and compute counterterms to give a finite renormalized bulk action and dual one point functions. Restricting to linear deformations we find additional counterterms to include the remaining sphere deformations which strongly deform the asymptotic behaviour.

hep-th↗