Higher Derivative Theories Research Articles

Viscosity bound for anisotropic superfluids in higher derivative gravity

In the present paper, based on the principles of gauge/gravity duality we analytically compute the shear viscosity to entropy (η/s) ratio corresponding to the super fluid phase in Einstein Gauss-Bonnet gravity. From our analysis we note that the ratio indeed receives a finite temperature correction below certain critical temperature (T < T c ). This proves the non universality of η/s ratio in higher derivative theories of gravity. We also compute the upper bound for the Gauss-Bonnet coupling (λ) corresponding to the symmetry broken phase and note that the upper bound on the coupling does not seem to change as long as we are close to the critical point of the phase diagram. However the corresponding lower bound of the η/s ratio seems to get modified due to the finite temperature effects.

Renormalization and unitarity in higher derivative and nonlocal gravity theories

We review and discuss higher derivative and nonlocal theories of quantum gravity focusing on their UV and unitarity properties. We first consider the general fourth-order gravitational action, then actions containing derivatives up to any given fixed order, and discuss their UV divergences, fixed points and concomitant unitarity issues. This leads to a more general discussion of "asymptotic safety" and unitarity, which motivates the introduction of nonlocal theories containing derivatives to all orders arising from the expansion of entire functions. For such theories good UV behavior is visible at any finite truncation, but unitarity emerges only when derivatives to all orders are included.

String-inspired infinite-derivative theories of gravity: A brief overview

In String Theory, there often appears a rather interesting class of higher derivative theories containing an infinite set of derivatives in the form of an exponential. These theories may provide a way to tame ultraviolet (UV) divergences without introducing ghost-like states. Here we provide a brief overview on the progress that has been made over the last decade to construct such infinite-derivative theories of gravity (IDG) which may be able to address the singularity problems in gravity. In the process, we will present some general results that applies to covariant torsion-free metric theories of gravity.

Tulczyjew triples in higher derivative field theory

The geometrical structure known as Tulczyjew triple has been used with success in analytical mechanics and first order field theory to describe a wide range of physical systems including Lagrangian/Hamiltonian systems with constraints and/or sources, or with singular Lagrangian. Starting from the first principles of the variational calculus we derive Tulczyjew triples for classical field theories of arbitrary high order, i.e. depending on arbitrary high derivatives of the fields. A first triple appears as the result of considering higher order theories as first order ones with configurations being constrained to be holonomic jets. A second triple is obtained after a reduction procedure aimed at getting rid of nonphysical degrees of freedom. This picture we present is fully covariant and complete: it contains both Lagrangian and Hamiltonian formalisms, in particular the Euler-Lagrange equations. Notice that, the required Geometry of jet bundles is affine (as opposed to the linear Geometry of the tangent bundle). Accordingly, the notions of affine duality and affine phase space play a distinguished role in our picture. In particular the Tulczyjew triples in this paper consist of morphisms of double affine-vector bundles which, moreover, preserve suitable presymplectic structures.

Modified Hamiltonian Formalism for Regge-Teitelboim Cosmology

The Ostrogradski approach for the Hamiltonian formalism of higher derivative theory is not satisfactory because the Lagrangian cannot be viewed as a function on the tangent bundle to coordinate manifold. In this paper, we have used an alternative approach which leads directly to the Lagrangian which, being a function on the tangent manifold, gives correct equation of motion; no new coordinate variables need to be added. This approach can be used directly to the singular (in Ostrogradski sense) Lagrangian. We have used this method for the Regge-Teitelboim (RT) minisuperspace cosmological model. We have obtained the Hamiltonian of the dynamical equation of the scale factor of RT model.

Noncommutative Chern-Simons gauge and gravity theories and their geometric Seiberg-Witten map

We use a geometric generalization of the Seiberg-Witten map between noncommutative and commutative gauge theories to find the expansion of noncommutative Chern-Simons (CS) theory in any odd dimension $D$ and at first order in the noncommutativity parameter $\theta$. This expansion extends the classical CS theory with higher powers of the curvatures and their derivatives. A simple explanation of the equality between noncommutative and commutative CS actions in $D=1$ and $D=3$ is obtained. The $\theta$ dependent terms are present for $D\geq 5$ and give a higher derivative theory on commutative space reducing to classical CS theory for $\theta\to 0$. These terms depend on the field strength and not on the bare gauge potential. In particular, as for the Dirac-Born-Infeld action, these terms vanish in the slowly varying field strength approximation: in this case noncommutative and commutative CS actions coincide in any dimension. The Seiberg-Witten map on the $D=5$ noncommutative CS theory is explored in more detail, and we give its second order $\theta$-expansion for any gauge group. The example of extended $D=5$ CS gravity, where the gauge group is $SU(2,2)$, is treated explicitly.

Super-renormalizable and finite gravitational theories

We hereby introduce and extensively study a class of non-polynomial higher derivative theories of gravity that realize a ultraviolet (UV) completion of Einstein general relativity. These theories are unitary (ghost free) and at most only one-loop divergences survive. The outcome is a class of theories super-renormalizable in even dimension and finite in odd dimension. Moreover, we explicitly prove in D=4 that there exists an extension of the theory that is completely finite and all the beta functions vanish even at one-loop. These results can be easily extended in extra dimensions and it is likely that the higher dimensional theory can be made finite, too. Therefore we have the possibility for “finite quantum gravity” in any dimension.

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.

On entanglement entropy functionals in higher-derivative gravity theories

In arXiv:1310.5713 and arXiv:1310.6659 a formula was proposed as the entanglement entropy functional for a general higher-derivative theory of gravity, whose lagrangian consists of terms containing contractions of the Riemann tensor. In this paper, we carry out some tests of this proposal. First, we find the surface equation of motion for general four-derivative gravity theory by minimizing the holographic entanglement entropy functional resulting from this proposed formula. Then we calculate the surface equation for the same theory using the generalized gravitational entropy method of arXiv:1304.4926. We find that the two do not match in their entirety. We also construct the holographic entropy functional for quasi-topological gravity, which is a six-derivative gravity theory. We find that this functional gives the correct universal terms. However, as in the four-derivative case, the generalized gravitational entropy method applied to this theory does not give exactly the surface equation of motion coming from minimizing the entropy functional.

Higher-derivative non-Abelian gauge fields via the Faddeev–Jackiw formalism

In this paper we analyze two higher-derivative theories, the generalized electrodynamics and the Alekseev–Arbuzov–Baikov effective Lagrangian from the point of view of the Faddeev–Jackiw symplectic approach. It is shown that the full set of constraints is obtained directly from the zero-mode eigenvectors, and that they are in accordance with well-known results from Dirac’s theory, a recurrent issue in the literature. The method shows to be rather economical in relation to the Dirac one, obviating thus unnecessary classification and calculations. Afterwards, to conclude we construct the transition amplitude of the non-Abelian theory following a constrained BRST method.

Extended massive gravity in three dimensions

Using a first order Chern-Simons-like formulation of gravity we systematically construct higher-derivative extensions of general relativity in three dimensions. The construction ensures that the resulting higher-derivative gravity theories are free of scalar ghosts. We canonically analyze these theories and construct the gauge generators and the boundary central charges. The models we construct are all consistent with a holographic c-theorem which, however, does not imply that they are unitary. We find that Born-Infeld gravity in three dimensions is contained within these models as a subclass.

Canonical structure of higher derivative theories

The canonical structure of theories whose Lagrangian contains higher powers of time derivatives is often obscured by the nonlinear relationship between the velocities and momenta. We use the Dirac formalism and define a generalized Legendre transform to overcome some of the difficulties associated with inverting the relation between velocities and momenta. We are then able to define a standard single valued symplectic structure on phase space and a compatible single valued Hamiltonian. We demonstrate the application of our formalism in several examples.

On the one-loop effective potential in the higher-derivative four-dimensional chiral superfield theory with a nonconventional kinetic term

We explicitly calculate the one-loop effective potential for a higher-derivative four-dimensional chiral superfield theory with a nonconventional kinetic term. We consider the cases of minimal and nonminimal general Lagrangians. In particular, we find that in the minimal case the divergent part of the one-loop effective potential vanishes by reason of the chirality.

Spontaneous generation of a crystalline ground state in a higher derivative theory

The possibility of Spontaneous Symmetry Breaking in momentum space in a generic Lifshitz scalar model–a non-relativistic scalar field theory with higher spatial derivative terms–has been studied. We show that the minimum energy state, the ground state, has a lattice structure, where the translation invariance of the continuum theory is reduced to a discrete translation symmetry. The scale of translation symmetry breaking (or induced lattice spacing) is proportional to the inverse of the momentum of the condensate particle. The crystalline ground state is stable under excitations below a certain critical velocity. The small fluctuations above the ground state can have a phonon like dispersion under suitable choice of parameters.At the beginning we have discussed the effects of next to nearest neighbor interaction terms in a model of linear triatomic molecule depicted by a linear system of three particles of same mass connected by identical springs. This model is relevant since in the continuum limit the next to nearest neighbor interaction terms generate higher (spatial) derivative wave equation, the main topic of this paper.

Do we have unitary and (super)renormalizable quantum gravity below the Planck scale?

We explore how the stability of metric perturbations in higher derivative theories of gravity depends on the energy scale of initial seeds of such perturbations and on a typical energy scale of the gravitational vacuum background. It is shown that, at least in the cases of specific cosmological backgrounds, that the unphysical massive ghost which is present in the spectrum of such theories is not growing up as a physical excitation and remains in the vacuum state, until the initial frequency of the perturbation is close to the Planck order of magnitude. In this situation the existing versions of renormalizable and superrenormalizable theories can be seen as very satisfactory effective theories of Quantum Gravity below the Planck scale.

Generic higher-derivativeN=2,d=3gauge theory

We formulate a generic $\mathcal{N}=2$ three-dimensional superfield higher-derivative gauge theory coupled to the matter, which, in certain cases reduces to the $\mathcal{N}=2$ three-dimensional scalar super-QED, or supersymmetric Maxwell-Chern-Simons or Chern-Simons theories with matter. For this theory, we explicitly calculate the one-loop effective potential.

Extremal surfaces and entanglement entropy

We have obtained the equation of the extremal hypersurface by considering the Jacobson–Myers functional and computed the entanglement entropy. In this context, we show that the higher derivative corrected extremal surfaces cannot penetrate the horizon. Also, we have studied the entanglement temperature and entanglement entropy for low excited states for such higher derivative theories when the entangling region is of the strip type.

Constraining models of f(R) gravity with Planck and WiggleZ power spectrum data

In order to explain cosmic acceleration without invoking ``dark'' physics, we consider f(R) modified gravity models, which replace the standard Einstein-Hilbert action in General Relativity with a higher derivative theory. We use data from the WiggleZ Dark Energy survey to probe the formation of structure on large scales which can place tight constraints on these models. We combine the large-scale structure data with measurements of the cosmic microwave background from the Planck surveyor. After parameterizing the modification of the action using the Compton wavelength parameter B0, we constrain this parameter using ISiTGR, assuming an initial non-informative log prior probability distribution of this cross-over scale. We find that the addition of the WiggleZ power spectrum provides the tightest constraints to date on B0 by an order of magnitude, giving log10(B0) < −4.07 at 95% confidence limit. Finally, we test whether the effect of adding the lensing amplitude ALens and the sum of the neutrino mass ∑mν is able to reconcile current tensions present in these parameters, but find f(R) gravity an inadequate explanation.

New Hamiltonian analysis of Regge-Teitelboim minisuperspace cosmology

A new Hamiltonian formulation of the minisuperspace cosmology following from the geodetic brane gravity model introduced by Regge and Teitelboim is presented. The model is considered in the framework of higher derivative theories which facilitates Hamiltonian formulation. The analysis is done using the equivalent first order approach. The constraint algebra is shown to realize a truncated Virasoro algebra. The gauge generator containing the exact number of gauge parameters is constructed. Equivalence between the gauge and reparametrization symmetries has been demonstrated. Complete gauge fixed computations have been provided and formal quantization is indicated.

On generalized gravitational entropy, squashed cones and holography

We consider generalized gravitational entropy in various higher derivative theories of gravity dual to four dimensional CFTs using the recently proposed regularization of squashed cones. We derive the universal terms in the entanglement entropy for spherical and cylindrical surfaces. This is achieved by constructing the Fefferman-Graham expansion for the leading order metrics for the bulk geometry and evaluating the generalized gravitational entropy. We further show that the Wald entropy evaluated in the bulk geometry constructed for the regularized squashed cones leads to the correct universal parts of the entanglement entropy for both spherical and cylindrical entangling surfaces. We comment on the relation with the Iyer-Wald formula for dynamical horizons relating entropy to a Noether charge. Finally we show how to derive the entangling surface equation in Gauss-Bonnet holography.