Entanglement entropy in higher derivative holography

We consider holographic entanglement entropy in higher derivative gravity theories. Recently Lewkowycz and Maldacena 1] have provided a method to derive the equations for the entangling surface from first principles. We use this method to compute the entangling surface in four derivative gravity. Certain interesting differences compared to the two derivative case are pointed out. For Gauss-Bonnet gravity, we show that in the regime where this method is applicable, the resulting equations coincide with proposals in the literature as well as with what follows from considerations of the stress tensor on the entangling surface. Finally we demonstrate that the area functional in Gauss-Bonnet holography arises as a counterterm needed to make the Euclidean action free of power law divergences.

Cordas cósmicas e gravitação planar de ordem superior

The possibility of generalizing gravity in 2+1 dimensions to include higher-derivative terms, thereby allowing for a dynamical theory, opens up a variety of new interesting questions. This is in great contrast with pure Einstein gravity which is a generally covariant theory that has no degrees of freedom - a peculiarity that, in a sense, renders it a little insipid and odorless. The research on gravity of particles moving in a plane, that is, living in flatland, within the context of higher-derivative gravity, leads to novel and interesting effects. For instance, the generation of gravity, antigravity, and gravitational shielding by the interaction of massive scalar bosons via a graviton exchange. In addition, the gravitational deffection angle of a photon, unlike that of Einstein gravity, is dependent of the impact parameter. On the other hand, the great drawback to using linearized general relativity for describing a gravitating string is that this description leads to some unphysical results such as: (i) lack of a gravity force in the nonrelativistic limit; (ii) gravitational deffection independent of the impact parameter. Interesting enough, the effective cure for these pathologies is the replacement of linearized gravity by linearized higher-derivative gravity. We address these issues here

Hall viscosity to entropy ratio in higher derivative theories

In this paper based on the basic principles of gauge/gravity duality we compute the hall viscosity to entropy ratio in the presence of various higher derivative corrections to the dual gravitational description embedded in an asymptotically AdS(4) space time. As the first step of our analysis, considering the back reaction we impose higher derivative corrections to the abelian gauge sector of the theory where we notice that the ratio indeed gets corrected at the leading order in the coupling. Considering the probe limit as a special case we compute this leading order correction over the fixed background of the charged black brane solution. Finally we consider higher derivative (R-2) correction to the gravity sector of the theory where we notice that the above ratio might get corrected at the sixth derivative level.

Gauge formulation for higher order gravity

This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained that includes derivatives of the curvature. We analyze the form of the second field strength, G=partial derivative F+fAF, in terms of geometrical variables. All possible independent Lagrangians constructed with quadratic contractions of F and quadratic contractions of G are analyzed. The equations of motion for a particular Lagrangian, which is analogous to Podolsky's term of his generalized electrodynamics, are calculated. The static isotropic solution in the linear approximation was found, exhibiting the regular Newtonian behavior at short distances as well as a meso-large distance modification.

Dimensional reduction of the massless limit of the linearized 'New Massive Gravity'

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Boson-boson effective nonrelativistic potential for higher-derivative electromagnetic theories in D dimensions

The problem of computing the effective nonrelativistic potential U-D for the interaction of charged-scalar bosons, within the context of D-dimensional electromagnetism with a cutoff, is reduced to quadratures. It is shown that U-3 cannot bind a pair of identical charged-scalar bosons; nevertheless, numerical calculations indicate that boson-boson bound states do exist in the framework of three-dimensional higher-derivative electromagnetism augmented by a topological Chern-Simons term.

Quadratic gravity theories in 2+1 dimensions and the topological Chern-Simons term

The addition of a topological Chern-Simons term to three-dimensional higher-derivative gravity is not a good therapy to cure the nonunitarity of the aforementioned theory. Moreover, R+R-2 gravity in (2+1)D, which is unitary at the tree level, becomes tree-level nonunitary when it is augmented by the abovementioned topological term. Therefore, unlike what is claimed in the literature, topological higher-derivative gravity in (2+1)D is not tree-level unitary and neither is topological three-dimensional R+R-2 gravity.

Unavoidable conflict between massive gravity models and massive topological terms

Massive gravity models in (2 + 1) dimensions, such as those obtained by adding to Einstein's gravity the usual Fierz-Pauli, or the more complicated Ricci scalar squared (R-2), terms, are tree level unitary. Interesting enough these seemingly harmless systems have their unitarity spoiled when they are augmented by a Chern-Simons term. Furthermore, if the massive topological term is added to R + R-munu(2) gravity, or to R + R-munu(2), + R-2 gravity (higher-derivative gravity), which are nonunitary at the tree level, the resulting models remain nonunitary. Therefore, unlike the common belief, as well as the claims in the literature, the coexistence between three-dimensional massive gravity models and massive topological terms is conflicting.

LIMITS on THE COUPLING CONSTANT of HIGHER-DERIVATIVE ELECTROMAGNETISM

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Investigations in massive 3D gravity

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

HIGHER-DERIVATIVE SCHWINGER MODEL

Using the operator formalism, we obtain the bosonic representation for the free fermion field satisfying an equation of motion with higher-order derivatives. Then, we consider the operator solution of a generalized Schwinger model with higher-derivative coupling. Since the increasing of the derivative order implies the introduction of an equivalent number of extra fermionic degrees of freedom, the mass acquired by the gauge field is bigger than the one for the standard two-dimensional QED. An analysis of the problem from the functional integration point of view corroborates the findings of canonical quantization, and corrects certain results previously announced in the literature on the basis of Fujikawa's technique.

New higher-derivative R-4 theorems for graviton scattering

The nonminimal pure spinor formalism for the superstring is used to prove two new multiloop theorems which are related to recent higher-derivative R-4 conjectures of Green, Russo, and Vanhove. The first theorem states that when 0 < n < 12, partial derivative R-n(4) terms in the Type II effective action do not receive perturbative contributions above n/2 loops. The second theorem states that when n <= 8, perturbative contributions to partial derivative R-n(4) terms in the IIA and IIB effective actions coincide. As shown by Green, Russo, and Vanhove, these results suggest that d=4 N=8 supergravity is ultraviolet finite up to eight loops.

Consistent higher derivative quantum field theory: A model without tachyons and ghosts

We present a higher derivative gauge theory in (2 + 1) dimensions which can have its parameters suitably tuned in order to become a consistent quantum field theory, in the sense that both tachyons and ghosts are absent from the particle spectrum of the theory.

Collective scattering of massive stars in higher order gravity

In the weak field approximation of higher order gravity theory a gravitational potential is described by a Newtonian plus a Yukawa-like term. This new term is used to explain some aspects of galactic dynamics, without considering dark matter. Its presence modifies the scattering probability of a massive intruder star and relaxation time of the stellar system.