Higher Derivative Theories Research Articles

Generalised boundary terms for higher derivative theories of gravity

In this paper we wish to find the corresponding Gibbons-Hawking-York term for the most general quadratic in curvature gravity by using Coframe slicing within the Arnowitt-Deser-Misner (ADM) decomposition of spacetime in four dimensions. In order to make sure that the higher derivative gravity is ghost and tachyon free at a perturbative level, one requires infinite covariant derivatives, which yields a generalised covariant infinite derivative theory of gravity. We will be exploring the boundary term for such a covariant infinite derivative theory of gravity.

Exorcising the Ostrogradsky ghost in coupled systems

The Ostrogradsky theorem implies that higher-derivative terms of a single mechanical variable are either trivial or lead to additional, ghost-like degrees of freedom. In this letter we systematically investigate how the introduction of additional variables can remedy this situation. Employing a Lagrangian analysis, we identify conditions on the Lagrangian to ensure the existence of primary and secondary constraints that together imply the absence of Ostrogradsky ghosts. We also show the implications of these conditions for the structure of the equations of motion as well as possible redefinitions of the variables. We discuss applications to analogous higher-derivative field theories such as multi-Galileons and beyond Horndeski.

BRST symmetry for Regge–Teitelboim-based minisuperspace models

The Einstein-Hilbert action in the context of Higher derivative theories is considered for finding out their BRST symmetries. Being a constraint system, the model is transformed in the minisuperspace language with the FRLW background and the gauge symmetries are explored. Exploiting the first order formalism developed by Banerjee et. al. the diffeomorphism symmetry is extracted. From the general form of the gauge transformations of the field, the analogous BRST transformations are calculated. The effective Lagrangian is constructed by considering two gauge fixing conditions. Further, the BRST (conserved) charge is computed which plays an important role in defining the physical states from the total Hilbert space of states. The finite field dependent BRST (FFBRST) formulation is also studied in this context where the Jacobian for functional measure is illustrated specifically.

High-energy scatterings in infinite-derivative field theory and ghost-free gravity

In this paper, we will consider scattering diagrams in the context of infinite-derivative theories. First, we examine a finite-order, higher-derivative scalar field theory and find that we cannot eliminate the growth of scattering diagrams for large external momenta. Then, we employ an infinite-derivative scalar toy model and obtain that the external momentum dependence of scattering diagrams is convergent as the external momenta become very large. In order to eliminate the external momentum growth, one has to dress the bare vertices of the scattering diagrams by considering renormalised propagator and vertex loop corrections to the bare vertices. Finally, we investigate scattering diagrams in the context of a scalar toy model which is inspired by a ghost-free and singularity-free infinite-derivative theory of gravity, where we conclude that infinite derivatives can eliminate the external momentum growth of scattering diagrams and make the scattering diagrams convergent in the ultraviolet.

Higher-order theories from the minimal length

We show that the introduction of a minimal length in the context of noncommutative space–time gives rise (after some considerations) to higher-order theories. We then explicitly demonstrate how these higher-derivative theories appear as a generalization of the standard electromagnetism and general relativity by applying a consistent procedure that modifies the original Maxwell and Einstein–Hilbert actions. In order to set a bound on the minimal length, we compare the deviations from the inverse-square law with the potentials obtained in the higher-order theories and discuss the validity of the results. The introduction of a quantum bound for the minimal length parameter [Formula: see text] in the higher-order QED allows us to lower the actual limits on the parameters of higher-derivative gravity by almost half of their order of magnitude.

Super-renormalizable or finite Lee–Wick quantum gravity

We propose a class of multidimensional higher derivative theories of gravity without extra real degrees of freedom besides the graviton field. The propagator shows up the usual real graviton pole in k2=0 and extra complex conjugates poles that do not contribute to the absorptive part of the physical scattering amplitudes. Indeed, they may consistently be excluded from the asymptotic observable states of the theory making use of the Lee–Wick and Cutkosky, Landshoff, Olive and Polkinghorne prescription for the construction of a unitary S-matrix. Therefore, the spectrum consists of the graviton and short lived elementary unstable particles that we named “anti-gravitons” because of their repulsive contribution to the gravitational potential at short distance. However, another interpretation of the complex conjugate pairs is proposed based on the Calmet's suggestion, i.e. they could be understood as black hole precursors long established in the classical theory. Since the theory is CPT invariant, the conjugate complex of the micro black hole precursor can be interpreted as a white hole precursor consistently with the 't Hooft complementarity principle. It is proved that the quantum theory is super-renormalizable in even dimension, i.e. only a finite number of divergent diagrams survive, and finite in odd dimension. Furthermore, turning on a local potential of the Riemann tensor we can make the theory finite in any dimension. The singularity-free Newtonian gravitational potential is explicitly computed for a range of higher derivative theories. Finally, we propose a new super-renormalizable or finite Lee–Wick standard model of particle physics.

Warped AdS3 black holes in higher derivative gravity theories

We consider warped AdS_3 black holes in generic higher derivatives gravity theories in 2+1 dimensions. The asymptotic symmetry group of the phase space containing these black holes is the semi-direct product of a centrally extended Virasoro algebra and an affine u(1) Kac-Moody algebra. Previous works have shown that in some specific theories, the entropy of these black holes agrees with a Cardy-like entropy formula derived for warped conformal field theories. In this paper, we show that this entropy matching continues to hold for the most general higher derivative theories of gravity. We also discuss the existence of phase transitions.

C T for non-unitary CFTs in higher dimensions

The coefficient $C_T$ of the conformal energy-momentum tensor two-point function is determined for the non-unitary scalar CFTs with four- and six-derivative kinetic terms. The results match those expected from large-$N$ calculations for the CFTs arising from the $O(N)$ non-linear sigma and Gross-Neveu models in specific even dimensions. $C_T$ is also calculated for the CFT arising from $(n-1)$-form gauge fields with derivatives in $2n+2$ dimensions. Results for $(n-1)$-form theory extended to general dimensions as a non-gauge-invariant CFT are also obtained; the resulting $C_T$ differs from that for the gauge-invariant theory. The construction of conformal primaries by subtracting descendants of lower-dimension primaries is also discussed. For free theories this also leads to an alternative construction of the energy-momentum tensor, which can be quite involved for higher-derivative theories.

RG flow and thermodynamics of causal horizons in higher-derivative AdS gravity

In arXiv:1508.01343 [hep-th], one of the authors proposed that in AdS/CFT the gravity dual of the boundary $c$-theorem is the second law of thermodynamics satisfied by causal horizons in AdS and this was verified for Einstein gravity in the bulk. In this paper we verify this for higher derivative theories. We pick up theories for which an entropy expression satisfying the second law exists and show that the entropy density evaluated on the causal horizon in a RG flow geometry is a holographic c-function. We also prove that given a theory of gravity described by a local covariant action in the bulk a sufficient condition to ensure holographic c-theorem is that the second law of causal horizon thermodynamics be satisfied by the theory. This allows us to explicitly construct holographic c-function in a theory where there is curvature coupling between gravity and matter and standard null energy condition cannot be defined although second law is known to hold. Based on the duality between c-theorem and the second law of causal horizon thermodynamics proposed in arXiv:1508.01343 [hep-th] and the supporting calculations of this paper we conjecture that every Unitary higher derivative theory of gravity in AdS satisfies the second law of causal horizon thermodynamics. If this is not true then c-theorem will be violated in a unitary Lorentz invariant field theory.

Minimal extension of Einstein’s theory: The quartic gravity

We study structure of solutions of the recently constructed minimal extensions of Einstein's gravity in four dimensions at the quartic curvature level. The extended higher derivative theory, just like Einstein's gravity, has only a massless spin-two graviton about its unique maximally symmetric vacuum. The extended theory does not admit the Schwarzschild or Kerr metrics as exact solutions, hence there is no issue of Schwarzschild type singularity but, approximately, outside a source, spherically symmetric metric with the correct Newtonian limit is recovered. We also show that for all Einstein space-times, square of the Riemann tensor (the Kretschmann scalar or the Gauss-Bonnet invariant) obeys a non-linear scalar Klein-Gordon equation.

Higher-derivative gravity with non-minimally coupled Maxwell field

We construct higher-derivative gravities with a non-minimally coupled Maxwell field. The Lagrangian consists of polynomial invariants built from the Riemann tensor and the Maxwell field strength in such a way that the equations of motion are second order for both the metric and the Maxwell potential. We also generalize the construction to involve a generic non-minimally coupled $p$-form field strength. We then focus on one low-lying example in four dimensions and construct the exact magnetically-charged black holes. We also construct exact electrically-charged $z=2$ Lifshitz black holes. We obtain approximate dyonic black holes for the small coupling constant or small charges. We find that the thermodynamics based on the Wald formalism disagrees with that derived from the Euclidean action procedure, suggesting this may be a general situation in higher-derivative gravities with non-minimally coupled form fields. As an application in the AdS/CFT correspondence, we study the entropy/viscosity ratio for the AdS or Lifshitz planar black holes, and find that the exact ratio can be obtained without having to know the details of the solutions, even for this higher-derivative theory.

Three-point functions in duality-invariant higher-derivative gravity

Doubled α′-geometry is the simplest higher-derivative gravitational theory with exact global duality symmetry. We use the double metric formulation of this theory to compute on-shell three-point functions to all orders in α′. A simple pattern emerges when comparing with the analogous bosonic and heterotic three-point functions. As in these theories, the amplitudes factorize. The theory has no Gauss-Bonnet term, but contains a Riemann-cubed interaction to second order in α′.

Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability

Theories with higher order time derivatives generically suffer from ghost-like instabilities, known as Ostrogradski instabilities. This fate can be avoided by considering ``degenerate'' Lagrangians, whose kinetic matrix cannot be inverted, thus leading to constraints between canonical variables and a reduced number of physical degrees of freedom. In this work, we derive in a systematic way the degeneracy conditions for scalar-tensor theories that depend quadratically on second order derivatives of a scalar field. We thus obtain a classification of all degenerate theories within this class of scalar-tensor theories. The quartic Horndeski Lagrangian and its extension beyond Horndeski belong to these degenerate cases. We also identify new families of scalar-tensor theories with the property that they are degenerate despite the nondegeneracy of the purely scalar part of their Lagrangian.

Hydrodynamics of a black brane in Gauss–Bonnet massive gravity

A black brane solution to Gauss–Bonnet massive gravity is introduced. In the context of AdS/CFT correspondence, the viscosity to entropy ratio is found by the Green–Kubo formula. The result indicates a violation of the well-known KSS bound, as expected in a higher derivative theory. Setting mass zero gives back the known viscosity to entropy ratio dependent on the Gauss–Bonnet coupling, while without the Gauss–Bonnet term, a nonzero mass parameter does not contribute to the ratio which saturates the bound of

Decoupling of heavy states in higher-derivative supersymmetric field theories

We study the problem of decoupling of heavy chiral superfields in four-dimensional $N=1$ supersymmetric field theories with Lorentz-invariant and Lorentz-violating higher-derivative terms. We demonstrate that the earlier found effect of large logarithmic quantum corrections, due to heavy chiral superfields, takes place not only if the theory possesses quantum divergences, but also for essentially finite theories involving higher derivative terms, both Lorentz-invariant and Lorentz-breaking ones.

Mass Gap for Black-Hole Formation in Higher-Derivative and Ghost-Free Gravity.

We study a spherical gravitational collapse of a small mass in higher-derivative and ghost-free theories of gravity. By boosting a solution of linearized equations for a static point mass in such theories we obtain in the Penrose limit the gravitational field of an ultrarelativistic particle. Taking a superposition of such solutions we construct a metric of a collapsing null shell in the linearized higher-derivative and ghost-free gravity. The latter allows one to find the gravitational field of a thick null shell. By analyzing these solutions we demonstrate that in a wide class of the higher dimensional theories of gravity as well as for the ghost-free gravity there exists a mass gap for mini-black-hole production. We also found conditions when the curvature invariants remain finite at r=0 for the collapse of the thick null shell.

A relation between deformed superspace and Lee–Wick higher-derivative theories

We propose a non-anticommutative superspace that relates to the Lee–Wick type of higher-derivative theories, which are known for their interesting properties and have led to proposals of phenomenologically viable higher-derivative extensions of the Standard Model. The deformation of superspace we consider does not preserve supersymmetry or associativity in general, but, we show that a non-anticommutative version of the Wess–Zumino model can be properly defined. In fact, the definition of chiral and antichiral superfields turns out to be simpler in our case than in the well known supersymmetric case. We show that when the theory is truncated at the first nontrivial order in the deformation parameter, supersymmetry is restored, and we end up with a well-known Lee–Wick type of higher-derivative extension of the Wess–Zumino model. Thus, we show how non-anticommutativity could provide an alternative mechanism for generating these higher-derivative theories.

Quantum fluctuations and thermal dissipation in higher derivative gravity

In this paper, based on the AdS2/CFT1 prescription, we explore the low frequency behavior of quantum two point functions for a special class of strongly coupled CFTs in one dimension whose dual gravitational counterpart consists of extremal black hole solutions in higher derivative theories of gravity defined over an asymptotically AdS spacetime. The quantum critical points thus described are supposed to correspond to a very large value of the dynamic exponent (z→∞). In our analysis, we find that quantum fluctuations are enhanced due to the higher derivative corrections in the bulk which in turn increases the possibility of quantum phase transition near the critical point. On the field theory side, such higher derivative effects would stand for the corrections appearing due to the finite coupling in the gauge theory. Finally, we compute the coefficient of thermal diffusion at finite coupling corresponding to Gauss Bonnet corrected charged Lifshitz black holes in the bulk. We observe an important crossover corresponding to z=5 fixed point.

On Newtonian singularities in higher derivative gravity models

We consider the problem of Newtonian singularity in the wide class of higher derivative gravity models, including the ones which are renormalizable and super-renormalizable at the quantum level. The simplest version of the singularity-free theory has four derivatives and is pretty well-known. We argue that in all cases of local higher-derivative theories, when the poles of the propagator are real and simple, the singularities disappear due to the cancellation of contributions from scalar and tensor massive modes.

Standard model and graviweak unification with (super)renormalizable gravity. Part I: Visible and invisible sectors of the universe

We develop a self-consistent Spin (4, 4)-invariant model of the unification of gravity with weak SU(2) gauge and Higgs fields in the visible and invisible sectors of our universe. We consider a general case of the graviweak unification, including the higher-derivative super-renormalizable theory of gravity, which is a unitary, asymptotically-free and perturbatively consistent theory of the quantum gravity.