Counting ghosts in the "ghost-free" non-local gravity

Abstract

In the recently proposed non-local theory of quantum gravity one can avoid massive tensor ghosts at the tree level by a special choice of the non-local form factor between the two Ricci tensors. We show that at the quantum level this theory has an infinite amount of massive unphysical states, mostly corresponding to complex poles.

18 pages, LaTeX. Section 5 discuss relation between renormalization and Newtonian limit and includes a note concerning recent comment on our previous preprint by Biswas et al in arXive:1412.3467. The new version includes many technical explanations added due to the advises of the anonymous referee. Wording is also shortened. Fits the version accepted in Physics Letters B

References in corpus (20)

• Towards singularity and ghost free theories of gravity
• Super-renormalizable Quantum Gravity
• Super-renormalizable & Finite Gravitational Theories
• Some remarks on high derivative quantum gravity
• Effective Action of Vacuum: Semiclassical Approach
• On singularities of spherically symmetric backgrounds in string theory
• Renormalization Group and Decoupling in Curved Space
• Superrenormalizable gauge and gravitational theories
• Do we have unitary and (super)renormalizable Quantum Gravity below Planck scale?
• Fusing multiple W states simultaneously with a Fredkin gate
• Renormalization Group and Decoupling in Curved Space: II. The Standard Model and Beyond
• Non-local massive gravity
• On Newtonian singularities in higher derivative gravity models
• On the Functional Renormalization Group approach for Yang-Mills fields
• The Newtonian limit of fourth and higher order gravity
• Nonlocal theories of gravity: the flat space propagator
• On the inflationary solutions in higher-derivative gravity with dilaton field
• Stringy gravity at short distances
• Super-renormalizable Multidimensional Quantum Gravity
• Vacuum contribution of photons in the theory with Lorentz and CPT-violating terms

Cited by in corpus (65)

• Superrenormalizable quantum gravity with complex ghosts
• Super-renormalizable or Finite Lee-Wick Quantum Gravity
• Universally Finite Gravitational & Gauge Theories
• Spacetime completeness of non-singular black holes in conformal gravity
• Low-energy effects in a higher-derivative gravity model with real and complex massive poles
• Nonlocal quantum gravity and M-theory
• Renormalization group in super-renormalizable quantum gravity
• Non-perturbative unitarity and fictitious ghosts in quantum gravity
• Finite Quantum Gravity Amplitudes -- no strings attached
• On Newtonian singularities in higher derivative gravity models
• On the gravitational seesaw in higher-derivative gravity
• On the cancellation of Newtonian singularities in higher-derivative gravity
• Gauge invariant renormalizability of quantum gravity
• Finite quantum gauge theories
• On the ghost-induced instability on de Sitter background
• Gauges and functional measures in quantum gravity II: Higher derivative gravity
• Effective delta sources and regularity in higher-derivative and ghost-free gravity
• Higher-order modified Starobinsky inflation
• On the Vilkovisky-DeWitt approach and renormalization group in effective quantum gravity
• Finite quantum gravity in dS and AdS spacetimes
• Black supernovae and black holes in non-local gravity
• Background field method and nonlinear gauges
• Radiation from an emitter in the ghost free scalar theory
• Weak-field limit and regular solutions in polynomial higher-derivative gravities
• Scalar model of effective field theory in curved space
• Ultrarelativistic spinning objects in non-local ghost-free gravity
• Gravitational Friedel oscillations in higher-derivative and infinite-derivative gravity?
• Higher-order regularity in local and nonlocal quantum gravity
• Scalar-multi-tensorial equivalence for higher order $f\left(R,{\nabla }_{\mu }R,{\nabla }_{{\mu }_1}{\nabla }_{{\mu }_2}R,...,{\nabla }_{{\mu }_1}...{\nabla }_{{\mu }_n}R\right)$ theories of gravity
• Ghost-free modification of the Polyakov action and Hawking radiation
• Probing the vacuum fluctuations in scalar ghost-free theories
• Lee-Wick Black Holes
• Tensor instabilities at the end of the LCDM universe
• $f(R,R_{\mu \nu }^2)$ at one loop
• Renormalization Group in Six-derivative Quantum Gravity
• $f\left(R,{\nabla }_{{\mu }_1}R,\dots ,{\nabla }_{{\mu }_1}\dots {\nabla }_{{\mu }_n}R\right)$ theories of gravity in Einstein frame: A higher order modified Starobinsky inflation model in the Palatini approach
• The Higgs mechanism in nonlocal field theory
• Rotating Lee-Wick Black Hole and Thermodynamics
• Retarded field of a uniformly accelerated source in non-local scalar field theory
• On thermal field fluctuations in ghost-free theories
• Deforming the Starobinsky model in ghost-free higher derivative supergravities
• Recent Progress in Fighting Ghosts in Quantum Gravity
• Towards a unitary, renormalizable and ultraviolet-complete quantum theory of gravity
• Finite Entanglement Entropy of Black Holes
• Asymptotic nonlocality
• Classical and Quantum Nonlocal Supergravity
• Interesting features of a general class of higher derivative theories of quantum gravity
• Effective approach to the Antoniadis-Mottola model: quantum decoupling of the higher derivative terms
• Renormalizability in $D$-dimensional higher-order gravity
• Spherically Symmetric Solutions in Higher-Derivative Theories of Gravity
• Interparticle potential energy for D-dimensional electromagnetic models from the corresponding scalar ones
• Non-perturbative Lee-Wick gauge theory: Towards Confinement and RGE with strong couplings
• Gauge invariant renormalizability of quantum gravity
• Renormalization of Einstein gravity through a derivative-dependent field redefinition
• Spherical collapse of small masses in the ghost-free gravity
• Deformations of the AdS-Schwarzschild black brane and the shear viscosity of the quark-gluon plasma
• The origin of regular Newtonian potential in infinite derivative gravity
• Generalized extremal branes in AdS/CMT and holographic superconductors
• Causality, unitarity and stability in quantum gravity: a non-perturbative perspective
• Ghost-free higher derivative unimodular gravity
• Nonlocal scalar field in an external potential: WKB approximation
• The background information about perturbative quantum gravity
• Smearing out contact terms in ghost-free infinite derivative quantum gravity
• Conditions for positivity of energy in superrenormalizable polynomial gravity
• Limiting fluctuations in quantum gravity to diffeomorphisms