22 research outputs found
The Status of Horava Gravity
Horava gravity is a proposal for a UV completion of gravitation obtained by
endowing the space-time manifold with a preferred foliation in space-like
hypersurfaces. This allows for a power-counting renormalizable theory free of
ghosts, at the cost of breaking local Lorentz invariance and diffeomorphism
invariance down to foliation preserving transformations. In this updated
review, we report the main successes and challenges of the proposal, discussing
the main features of the projectable and non-projectable versions of Ho\v rava
gravity. We focus in three main aspects: (i) the UV regime, discussing the
renormalizability and renormalization group flow of the projectable theory, as
well as the obstacles towards similar results in the non-projectable case; (ii)
the low energy phenomenology of both models, including the PN regime, the most
updated constraints in the parameter space of the theory, the structure of
black holes at low energies, and the possibility of dark matter emerging from
gravitational dynamics in the projectable model; and (iii) the specific
phenomena induced by higher derivatives, such as the possibility of
regularizing singularities, the dynamical behavior of solutions to dispersive
equations, and the emission of Hawking radiation by universal horizons.Comment: Invited review for the EPJP special issue on Higher Derivatives in
Quantum Gravity. 49 pages, 2 figures. Comments are welcom
Renormalization of Horava Gravity
We prove perturbative renormalizability of projectable Horava gravity. The
key element of the argument is the choice of a gauge which ensures the correct
anisotropic scaling of the propagators and their uniform falloff at large
frequencies and momenta. This guarantees that the counterterms required to
absorb the loop divergences are local and marginal or relevant with respect to
the anisotropic scaling. Gauge invariance of the counterterms is achieved by
making use of the background-covariant formalism. We also comment on the
difficulties of this approach when addressing the renormalizability of the
non-projectable model.Comment: 35 pages, no figures; references discussing gauge invariance of
counterterms have been added, typos correcte
UV graviton scattering and positivity bounds from IR dispersion relations
Scattering amplitudes mediated by graviton exchange display IR singularities
in the forward limit. This obstructs standard application of positivity bounds
based on twice subtracted dispersion relations. Such divergences can be
cancelled only if the UV limit of the scattering amplitude behaves in a
specific way, which implies a very non-trivial connection between the UV and IR
behaviors of the amplitude. We show that this relation can be expressed in
terms of an integral transform, obtaining analytic results when . Carefully applying this limit to dispersion relations,
we find that infinite arc integrals, which are usually taken to vanish, can
give a non-trivial contribution in the presence of gravity, unlike in the case
of finite negative . This implies that gravitational positivity bounds
cannot be trusted unless the size of this contribution is estimated in some
way, which implies assumptions on the UV completion of gravitational
interactions. We discuss the relevance of these findings in the particular case
of QED coupled to gravity.Comment: 20 pages, 2 figure
Renormalization of gauge theories in the background-field approach
Using the background-field method we demonstrate the
Becchi-Rouet-Stora-Tyutin (BRST) structure of counterterms in a broad class of
gauge theories. Put simply, we show that gauge invariance is preserved by
renormalization in local gauge field theories whenever they admit a sensible
background-field formulation and anomaly-free path integral measure. This class
encompasses Yang-Mills theories (with possibly Abelian subgroups) and
relativistic gravity, including both renormalizable and non-renormalizable
(effective) theories. Our results also hold for non-relativistic models such as
Yang-Mills theories with anisotropic scaling or Horava gravity. They strengthen
and generalize the existing results in the literature concerning the
renormalization of gauge systems. Locality of the BRST construction is
emphasized throughout the derivation. We illustrate our general approach with
several explicit examples.Comment: 45 pages, no figures; references added, changes in the Introduction
and Conclusion
Ho\v{r}ava gravity is asymptotically free (in 2+1 dimensions)
We compute the -functions of marginal couplings in projectable
Ho\v{r}ava gravity in spacetime dimensions. We show that the
renormalization group flow has an asymptotically-free fixed point in the
ultraviolet (UV), establishing the theory as a UV-complete model with dynamical
gravitational degrees of freedom. Therefore, this theory may serve as a
toy-model to study fundamental aspects of quantum gravity. Our results
represent a step forward towards understanding the UV properties of realistic
versions of Ho\v{r}ava gravity.Comment: Updated references, minor revisions. Matches journal versio
Well-posed evolution of field theories with anisotropic scaling: the Lifshitz scalar field in a black hole space-time
Partial differential equations exhibiting an anisotropic scaling between
space and time -- such as those of Horava-Lifshitz gravity -- have a dispersive
nature. They contain higher-order spatial derivatives, but remain second order
in time. This is inconvenient for performing long-time numerical evolutions, as
standard explicit schemes fail to maintain convergence unless the time step is
chosen to be very small. In this work, we develop an implicit evolution scheme
that does not suffer from this drawback, and which is stable and second-order
accurate. As a proof of concept, we study the numerical evolution of a Lifshitz
scalar field on top of a spherically symmetric black hole space-time. We
explore the evolution of a static pulse and an (approximately) ingoing
wave-packet for different strengths of the Lorentz-breaking terms, accounting
also for the effect of the angular momentum eigenvalue and the resulting
effective centrifugal barrier. Our results indicate that the dispersive terms
produce a cascade of modes that accumulate in the region in between the Killing
and universal horizons, indicating a possible instability of the latter.Comment: 22 pages, 8 figures, 1 table, comments are welcome
EuCAPT White Paper: Opportunities and Challenges for Theoretical Astroparticle Physics in the Next Decade
Astroparticle physics is undergoing a profound transformation, due to a
series of extraordinary new results, such as the discovery of high-energy
cosmic neutrinos with IceCube, the direct detection of gravitational waves with
LIGO and Virgo, and many others. This white paper is the result of a
collaborative effort that involved hundreds of theoretical astroparticle
physicists and cosmologists, under the coordination of the European Consortium
for Astroparticle Theory (EuCAPT). Addressed to the whole astroparticle physics
community, it explores upcoming theoretical opportunities and challenges for
our field of research, with particular emphasis on the possible synergies among
different subfields, and the prospects for solving the most fundamental open
questions with multi-messenger observations.Comment: White paper of the European Consortium for Astroparticle Theory
(EuCAPT). 135 authors, 400 endorsers, 133 pages, 1382 reference