Entanglement entropy of Wilson loops: Holography and matrix models

A half-BPS circular Wilson loop in $\mathcal{N}=4$ $SU(N)$ supersymmetric Yang-Mills theory in an arbitrary representation is described by a Gaussian matrix model with a particular insertion. The additional entanglement entropy of a spherical region in the presence of such a loop was recently computed by Lewkowycz and Maldacena using exact matrix model results. In this note we utilize the supergravity solutions that are dual to such Wilson loops in a representation with order $N^2$ boxes to calculate this entropy holographically. Employing the matrix model results of Gomis, Matsuura, Okuda and Trancanelli we express this holographic entanglement entropy in a form that can be compared with the calculation of Lewkowycz and Maldacena. We find complete agreement between the matrix model and holographic calculations.Comment: 17 pages, 1 figur

Lifshitz entanglement entropy from holographic cMERA

We study entanglement entropy in free Lifshitz scalar field theories holographically by employing the metrics proposed by Nozaki, Ryu and Takayanagi in \cite{Nozaki:2012zj} obtained from a continuous multi-scale entanglement renormalisation ansatz (cMERA). In these geometries we compute the minimal surface areas governing the entanglement entropy as functions of the dynamical exponent $z$ and we exhibit a transition from an area law to a volume law analytically in the limit of large $z$. We move on to explore the effects of a massive deformation, obtaining results for any $z$ in arbitrary dimension. We then trigger a renormalisation group flow between a Lifshitz theory and a conformal theory and observe a monotonic decrease in entanglement entropy along this flow. We focus on strip regions but also consider a disc in the undeformed theory.Comment: 17 pages, v2: references added and improved discussions, v3: published versio

On the convergence of Regge calculus to general relativity

Motivated by a recent study casting doubt on the correspondence between Regge calculus and general relativity in the continuum limit, we explore a mechanism by which the simplicial solutions can converge whilst the residual of the Regge equations evaluated on the continuum solutions does not. By directly constructing simplicial solutions for the Kasner cosmology we show that the oscillatory behaviour of the discrepancy between the Einstein and Regge solutions reconciles the apparent conflict between the results of Brewin and those of previous studies. We conclude that solutions of Regge calculus are, in general, expected to be second order accurate approximations to the corresponding continuum solutions.Comment: Updated to match published version. Details of numerical calculations added, several sections rewritten. 9 pages, 4 EPS figure

A brief review of Regge calculus in classical numerical relativity

We briefly review past applications of Regge calculus in classical numerical relativity, and then outline a programme for the future development of the field. We briefly describe the success of lattice gravity in constructing initial data for the head-on collision of equal mass black holes, and discuss recent results on the efficacy of Regge calculus in the continuum limit.Comment: 2 pages, submitted to the Proceedings of the IX Marcel Grossmann Meeting, Rome, July 2-8, 200

Holographic entanglement entropy of surface defects

We calculate the holographic entanglement entropy in type IIB supergravity solutions that are dual to half-BPS disorder-type surface defects in ${\cal N}=4$ Super Yang-Mills theory. The entanglement entropy is calculated for a ball-shaped region bisected by a surface defect. Using the bubbling supergravity solutions we also compute the expectation value of the defect operator. Combining our result with the previously-calculated one-point function of the stress tensor in the presence of the defect, we adapt the calculation of Lewkowycz and Maldacena to obtain a second expression for the entanglement entropy. Our two expressions agree up to an additional term, whose possible origin and significance is discussedComment: 41 pages. pdflatex, 3 figures. v2: typos corrected, reference corrected, some comments on CFT interpretation added. v3: references added, some clarification

Drude in D major

We study holographic momentum relaxation in the limit of a large number of spacetime dimensions D. For an axion model we find that momentum conservation is restored as D becomes large. To compensate we scale the strength of the sources with D so that momentum is relaxed even at infinite D. We analytically obtain the quasi-normal modes which control electric and heat transport, and give their frequencies in a 1/D expansion. We also obtain the AC thermal conductivity as an expansion in 1/D, which at leading order takes Drude form. To order 1/D our analytical result provides a reasonable approximation to the AC conductivity even at D=4, establishing large D as a practical method in this context. As a further application, we discuss the signature of the transition from coherent to incoherent behaviour known to exist in the system for finite D.Comment: 19 pages, 2 figure

Apparent horizons in simplicial Brill wave initial data

We construct initial data for a particular class of Brill wave metrics using Regge calculus, and compare the results to a corresponding continuum solution, finding excellent agreement. We then search for trapped surfaces in both sets of initial data, and provide an independent verification of the existence of an apparent horizon once a critical gravitational wave amplitude is passed. Our estimate of this critical value, using both the Regge and continuum solutions, supports other recent findings.Comment: 7 pages, 6 EPS figures, LaTeX 2e. Submitted to Class. Quant. Gra

Dual metal-insulator and insulator-insulator switching in nanoscale and Al doped VO<inf>2</inf>

Thin films of VO2 doped with aluminium, or with nanoscale grain sizes, have been produced. They display semiconductor resistive behaviour above the transition temperature Tc, but a metallic and plasmonic optical response. All samples optically switch over almost identical large ranges at the transition, but have quite variable resistive switching. At fixed grain size a rigorous new quantitative correlation is found between semiconductor resistivity below Tc and the activation energy above Tc as Al doping level varies. Large crystals doped with Al also display this dual behaviour. A possible mechanism is discussed involving fast local fluctuations on neighbouring V4+ ions involving transient dimers with no net spin. Such fluctuations would then need to interact and correlate their motion over the scale of a nanograin within the lifetime of the dimer excitation. © 2008 IOP Publishing Ltd

Temperature dependence of optical and transport properties in VO<inf>2</inf> with high temperature anomalies

Thermochromic VO2 is of interest for energy efficient glazing, and for fast telecommunications because it optically switches in the near IR. Despite extensive study several aspects of its apparently diverse behaviour have not been explained satisfactorily. The visible-NIR permittivity and dc electrical conductivity of high quality thin films of VO2, across the metal-insulator phase transition and well into the metallic phase to temperatures up to 100 °C above Tc are studied as a function of temperature and grain size. Experimental behaviour is partly explained with effective medium models, existing band structures and classical transport theory. Anomalies however include: unphysically fast relaxation rate, counter-intuitive and significant differences between optical and dc, and bulk and thin film parameters; and residual "non-metallic" features above the transition in highly oriented films. Residual, but transient high temperature d-electron singlet pairing on V dimers, which is sensitive to nanostructure, is examined as a source of some anomalies. © 2007 Elsevier B.V. All rights reserved