arXiv subjects

Marika Taylor

Publications and source records attributed to Marika Taylor.

At least 37 records · Page 2Linked to original sources

arXiv2016

Renormalized entanglement entropy

We develop a renormalization method for holographic entanglement entropy based on area renormalization of entangling surfaces. The renormalized entanglement entropy is derived for entangling surfaces in asymptotically locally anti-de Sitter spacetimes in general dimensions and for entangling surfaces in four dimensional holographic renormalization group flows. The renormalized entanglement entropy for disk regions in $AdS_4$ spacetimes agrees precisely with the holographically renormalized action for $AdS_4$ with spherical slicing and hence with the F quantity, in accordance with the Casini-Huerta-Myers map. We present a generic class of holographic RG flows associated with deformations by operators of dimension $3/2 < Δ< 5/2$ for which the F quantity increases along the RG flow, hence violating the strong version of the F theorem. We conclude by explaining how the renormalized entanglement entropy can be derived directly from the renormalized partition function using the replica trick i.e. our renormalization method for the entanglement entropy is inherited directly from that of the partition function. We show explicitly how the entanglement entropy counterterms can be derived from the standard holographic renormalization counterterms for asymptotically locally anti-de Sitter spacetimes.

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arXiv2016

Entanglement entropy in top-down models

We explore holographic entanglement entropy in ten-dimensional supergravity solutions. It has been proposed that entanglement entropy can be computed in such top-down models using minimal surfaces which asymptotically wrap the compact part of the geometry. We show explicitly in a wide range of examples that the holographic entanglement entropy thus computed agrees with the entanglement entropy computed using the Ryu-Takayanagi formula from the lower-dimensional Einstein metric obtained from reduction over the compact space. Our examples include not only consistent truncations but also cases in which no consistent truncation exists and Kaluza-Klein holography is used to identify the lower-dimensional Einstein metric. We then give a general proof, based on the Lewkowycz-Maldacena approach, of the top-down entanglement entropy formula.

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arXiv2016

Lifshitz holography

In this article we review recent progress on the holographic modelling of field theories with Lifshitz symmetry. We focus in particular on the holographic dictionary for Lifshitz backgrounds - the relationship between bulk fields and boundary operators, operator correlation functions and underlying geometrical structure. The holographic dictionary is essential in identifying the universality class of strongly coupled Lifshitz theories described by gravitational models.

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arXiv2015

Generalized entanglement entropy

We discuss two measures of entanglement in quantum field theory and their holographic realizations. For field theories admitting a global symmetry, we introduce a global symmetry entanglement entropy, associated with the partitioning of the symmetry group. This quantity is proposed to be related to the generalized holographic entanglement entropy defined via the partitioning of the internal space of the bulk geometry. The second measure of quantum field theory entanglement is the field space entanglement entropy, obtained by integrating out a subset of the quantum fields. We argue that field space entanglement entropy cannot be precisely realised geometrically in a holographic dual. However, for holographic geometries with interior decoupling regions, the differential entropy provides a close analogue to the field space entanglement entropy. We derive generic descriptions of such inner throat regions in terms of gravity coupled to massive scalars and show how the differential entropy in the throat captures features of the field space entanglement entropy.

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arXiv2015

Entanglement entropy and differential entropy for massive flavors

In this paper we compute the holographic entanglement entropy for massive flavors in the D3-D7 system, for arbitrary mass and various entangling region geometries. We show that the universal terms in the entanglement entropy exactly match those computed in the dual theory using conformal perturbation theory. We derive holographically the universal terms in the entanglement entropy for a CFT perturbed by a relevant operator, up to second order in the coupling; our results are valid for any entangling region geometry. We present a new method for computing the entanglement entropy of any top-down brane probe system using Kaluza-Klein holography and illustrate our results with massive flavors at finite density. Finally we discuss the differential entropy for brane probe systems, emphasising that the differential entropy captures only the effective lower-dimensional Einstein metric rather than the ten-dimensional geometry.

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arXiv2015

Towards a general fluid/gravity correspondence

We set up the construction of generic (d+2)-dimensional metrics corresponding to (d+1)-dimensional fluids, representing holographically the hydrodynamic regimes of the putative dual theories. We give general seed equilibrium metrics appropriate to generic bulk stress energy tensors and discuss the implications of conformal rescalings of the hypersurface on which the fluid is defined. We then show how to obtain the corresponding hydrodynamic metrics using a relativistic gradient expansion and discuss the integrability conditions of the resulting equations. The stress energy tensors of the resulting fluids, both at and away from equilibrium, satisfy a quadratic constraint. We interpret this constraint in terms of two possible equations of state for the fluid and show that only one of the two equations is physical. We illustrate our discussions with the example of the cutoff AdS fluid, for which we find the precise interpretation in terms of deformations of the UV conformal field theory. Finally we discuss the relation between the modern fluid/gravity approach taken in this paper and the earlier membrane paradigm.

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arXiv2014

Inhomogeneity simplified

We study models of translational symmetry breaking in which inhomogeneous matter field profiles can be engineered in such a way that black brane metrics remain isotropic and homogeneous. We explore novel Lagrangians involving square root terms and show how these are related to massive gravity models and to tensionless limits of branes. Analytic expressions for the DC conductivity and for the low frequency scaling of the optical conductivity in phenomenological models are derived, and the optical conductivity is studied in detail numerically. The square root Lagrangians are associated with linear growth in the DC resistivity with temperature and also lead to minima in the optical conductivity at finite frequency, suggesting that our models may capture many features of heavy fermion systems.

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arXiv2013

Lifshitz from AdS at finite temperature and top down models

We construct analytically an asymptotically Lifshitz black brane with dynamical exponent z=1+epsilon^2 in an Einstein-Proca model, where epsilon is a small parameter. In previous work we showed that the holographic dual QFT is a deformation of a CFT by the time component of a vector operator and the parameter epsilon is the corresponding deformation parameter. In the black brane background this operator additionally acquires a vacuum expectation value. We explain how the QFT Ward identity associated with Lifshitz invariance leads to a conserved mass and compute analytically the thermodynamic quantities showing that they indeed take the form implied by Lifshitz invariance. In the second part of the paper we consider top down Lifshitz models with dynamical exponent close to one and show that they can be understood in terms of vector deformations of conformal field theories. However, in all known cases, both the conformal field theory and its Lifshitz deformations have modes that violate the Breitenlohner-Freedman bound.

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arXiv2013

Lifshitz as a deformation of Anti-de Sitter

We consider holography for Lifshitz spacetimes with dynamical exponent z=1+epsilon^2, where epsilon is small. We show that the holographically dual field theory is a specific deformation of the relativistic CFT, corresponding to the z=1 theory. Treating epsilon as a small expansion parameter we set up the holographic dictionary for Einstein-Proca models up to order epsilon^2 in three and four bulk dimensions. We explain how renormalization turns the relativistic conformal invariance into non-relativistic Lifshitz invariance with dynamical exponent z=1+epsilon^2. We compute the two-point function of the conserved spin two current for the dual two-dimensional field theory and verify that it is Lifshitz invariant. Using only QFT arguments, we show that a particular class of deformations of CFTs generically leads to Lifshitz scaling invariance and we construct examples of such deformations.

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arXiv2013

Holographic d-wave superconductors

We construct top down models for holographic d-wave superfluids in which the order parameter is a charged spin two field in the bulk. Close to the transition temperature the condensed phase can be captured by a charged spin two field in an R-charged black hole background (downstairs picture) or equivalently by specific graviton perturbations of a spinning black brane (upstairs picture). We analyse the necessary conditions on the mass and the charge of the spin two field for a condensed phase to exist and we discuss the competition of the d-wave phase with other phases such as s-wave superfluids.

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arXiv2013

Higher derivative effects for 4d AdS gravity

Motivated by holography, we explore higher derivative corrections to four-dimensional Anti-de Sitter (AdS) gravity. We point out that in such a theory the variational problem is generically not well-posed given only a boundary condition for the metric. However, when one evaluates the higher derivative terms perturbatively on a leading order Einstein solution, the equations of motion are always second order and therefore the variational problem indeed requires only a boundary condition for the metric. The equations of motion required to compute the spectrum around the corrected background are still generically higher order, with the additional boundary conditions being associated with new operators in the dual conformal field theory. We discuss which higher derivative curvature invariants are expected to arise in the four-dimensional action from a top-down perspective and compute the corrections to planar AdS black holes and to the spectrum around AdS in various cases. Requiring that the dual theory is unitary strongly constrains the higher derivative terms in the action, as the operators associated with the extra boundary conditions generically have complex conformal dimensions and non-positive norms.

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arXiv2012

Holographic realization of gauge mediated supersymmetry breaking

The general gauge mediation scenario provides a framework in which properties of a visible sector with soft supersymmetry breaking are computed from current correlation functions in the supersymmetry breaking hidden sector. In this paper we will use holography to model strongly coupled hidden sectors by weakly curved geometries and describe how the current correlators relevant for general gauge mediation are computed by holographic methods. We illustrate the general setup by a toy example which captures most of the relevant features.

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arXiv2012

The relativistic fluid dual to vacuum Einstein gravity

We present a construction of a (d+2)-dimensional Ricci-flat metric corresponding to a (d+1)-dimensional relativistic fluid, representing holographically the hydrodynamic regime of a (putative) dual theory. We show how to obtain the metric to arbitrarily high order using a relativistic gradient expansion, and explicitly carry out the computation to second order. The fluid has zero energy density in equilibrium, which implies incompressibility at first order in gradients, and its stress tensor (both at and away from equilibrium) satisfies a quadratic constraint, which determines its energy density away from equilibrium. The entire dynamics to second order is encoded in one first order and six second order transport coefficients, which we compute. We classify entropy currents with non-negative divergence at second order in relativistic gradients. We then verify that the entropy current obtained by pulling back to the fluid surface the area form at the null horizon indeed has a non-negative divergence. We show that there are distinct near-horizon scaling limits that are equivalent either to the relativistic gradient expansion we discuss here, or to the non-relativistic expansion associated with the Navier-Stokes equations discussed in previous works. The latter expansion may be recovered from the present relativistic expansion upon taking a specific non-relativistic limit.

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arXiv2012

The holographic fluid dual to vacuum Einstein gravity

We present an algorithm for systematically reconstructing a solution of the (d+2)-dimensional vacuum Einstein equations from a (d+1)-dimensional fluid, extending the non-relativistic hydrodynamic expansion of Bredberg et al in arXiv:1101.2451 to arbitrary order. The fluid satisfies equations of motion which are the incompressible Navier-Stokes equations, corrected by specific higher derivative terms. The uniqueness and regularity of this solution is established to all orders and explicit results are given for the bulk metric and the stress tensor of the dual fluid through fifth order in the hydrodynamic expansion. We establish the validity of a relativistic hydrodynamic description for the dual fluid, which has the unusual property of having a vanishing equilibrium energy density. The gravitational results are used to identify transport coefficients of the dual fluid, which also obeys an interesting and exact constraint on its stress tensor. We propose novel Lagrangian models which realise key properties of the holographic fluid.

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arXiv2012

Holography for Einstein-Maxwell-dilaton theories from generalized dimensional reduction

We show that a class of Einstein-Maxwell-Dilaton (EMD) theories are related to higher dimensional AdS-Maxwell gravity via a dimensional reduction over compact Einstein spaces combined with continuation in the dimension of the compact space to non-integral values (`generalized dimensional reduction'). This relates (fairly complicated) black hole solutions of EMD theories to simple black hole/brane solutions of AdS-Maxwell gravity and explains their properties. The generalized dimensional reduction is used to infer the holographic dictionary and the hydrodynamic behavior for this class of theories from those of AdS. As a specific example, we analyze the case of a black brane carrying a wave whose universal sector is described by gravity coupled to a Maxwell field and two neutral scalars. At thermal equilibrium and finite chemical potential the two operators dual to the bulk scalar fields acquire expectation values characterizing the breaking of conformal and generalized conformal invariance. We compute holographically the first order transport coefficients (conductivity, shear and bulk viscosity) for this system.

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arXiv2011

Holography for chiral scale-invariant models

Deformation of any d-dimensional conformal field theory by a constant null source for a vector operator of dimension (d + z -1) is exactly marginal with respect to anisotropic scale invariance, of dynamical exponent z. The holographic duals to such deformations are AdS plane waves, with z=2 being the Schrodinger geometry. In this paper we explore holography for such chiral scale-invariant models. The special case of z=0 can be realized with gravity coupled to a scalar, and is of particular interest since it is related to a Lifshitz theory with dynamical exponent two upon dimensional reduction. We show however that the corresponding reduction of the dual field theory is along a null circle, and thus the Lifshitz theory arises upon discrete light cone quantization of an anisotropic scale invariant field theory.

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arXiv2011

Holography for Schrodinger backgrounds

We discuss holography for Schrodinger solutions of both topologically massive gravity in three dimensions and massive vector theories in (d+1) dimensions. In both cases the dual field theory can be viewed as a d-dimensional conformal field theory (two dimensional in the case of TMG) deformed by certain operators that respect the Schrodinger symmetry. These operators are irrelevant from the viewpoint of the relativistic conformal group but they are exactly marginal with respect to the non-relativistic conformal group. The spectrum of linear fluctuations around the background solutions corresponds to operators that are labeled by their scaling dimension and the lightcone momentum k_v. We set up the holographic dictionary and compute 2-point functions of these operators both holographically and in field theory using conformal perturbation theory and find agreement. The counterterms needed for holographic renormalization are non-local in the v lightcone direction.

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arXiv2010

AdS boundary conditions and the Topologically Massive Gravity/CFT correspondence

The AdS/CFT correspondence provides a new perspective on recurrent questions in General Relativity such as the allowed boundary conditions at infinity and the definition of gravitational conserved charges. Here we review the main insights obtained in this direction over the last decade and apply the new techniques to Topologically Massive Gravity. We show that this theory is dual to a non-unitary CFT for any value of its parameter mu and becomes a Logarithmic CFT at mu = 1.

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