Power-counting Renormalizable Theory Research Articles

I-Love-Q relations in Hořava-Lifshitz gravity

Ho\v{r}ava-Lifshitz gravity is an alternative theory to general relativity which breaks Lorentz invariance in order to achieve an ultraviolet complete and power-counting renormalizable theory of gravity. In the low energy limit, Ho\v{r}ava-Lifshitz gravity coincides with a vector-tensor theory known as khronometric gravity. The deviation of khronometric gravity from general relativity can be parametrized by three coupling constants: $\alpha$, $\beta$, and $\lambda$. Solar system experiments and gravitational wave observations impose stringent bounds on $\alpha$ and $\beta$, while $\lambda$ is still relatively unconstrained ($\lambda\lesssim 0.01$). In this paper, we study whether one can constrain this remaining parameter with neutron star observations through the universal I-Love-Q relations between the moment of inertia (I), the tidal Love number (Love), and the quadrupole moment (Q), which are insensitive to details in the nuclear matter equation of state. To do so, we perturbatively construct slowly-rotating and weakly tidally-deformed neutron stars in khronometric gravity. We find that the I-Love-Q relations are independent of $\lambda$ in the limit $(\alpha,\beta) \to 0$. Although some components of the field equations depend on $\lambda$, we show through induction and a post-Minkowskian analysis that slowly-rotating neutron stars do not depend on $\lambda$ at all. Tidally deformed neutron stars, on the other hand, are modified in khronometric gravity (though the usual Love number is not modified, as mentioned earlier), and there are potentially new, non-GR Love numbers, though their observability is unclear. These findings indicate that it may be difficult to constrain $\lambda$ with rotating/tidally-deformed neutron stars.

Observational constraints on the fractal cosmology

In this paper, we explore a fractal model of the universe proposed by Calcagni (J High Energy Phys 03:120, 2010) for a power-counting renormalizable field theory living in a fractal spacetime. Considering a timelike fractal profile, we derived field equations in fractal cosmology, in order to explore the structure formation and the expansion history in fractal universe. Numerical investigations based on matter power spectra diagrams report higher structure growth in fractal cosmology, being in contrast to local galaxy surveys. Additionally, according to the evolution of Hubble parameter diagrams, it can be understood that Hubble constant would decrease in fractal cosmology, which is also incompatible with low redshift estimations of H_0. So, concerning primary numerical studies, it seems that fractal cosmology is not capable to alleviate the tensions between local and global observational probes. Then, in pursuance of more accurate results, we constrain the fractal cosmology by observational data, including Planck cosmic microwave background (CMB), weak lensing, supernovae, baryon acoustic oscillations (BAO), and redshift-space distortions (RSD) data. The derived constraints on fractal dimension beta indicate that there is no considerable deviation from standard model of cosmology.

A new scalar–tensor realization of Hořava–Lifshitz gravity

We discuss a new covariant scalar–tensor system aimed to realise Hořava proposal for a power-counting renormalizable theory of gravity, with the special feature of not propagating scalar degrees of freedom in an appropriate gauge. The theory is characterized by a new symmetry acting on the metric, that can protect the particular form of its interactions. The set-up spontaneously breaks Lorentz symmetry by means of a time-like scalar field profile. By selecting a unitary gauge for the scalar, we show that this theory describes the dynamics of a spin two degree of freedom, whose equations of motion contain two time derivatives and up to six spatial derivatives. We analytically determine asymptotically flat, spherically symmetric configurations, showing that there exists a branch of solutions physically equivalent to spherically symmetric configurations in general relativity, also in the presence of matter fields.

Higgs potential from derivative interactions

A formulation of the linear [Formula: see text] model with derivative interactions is studied. The classical theory is on-shell equivalent to the [Formula: see text] model with the standard quartic Higgs potential. The mass of the scalar mode only appears in the quadratic part and not in the interaction vertices, unlike in the ordinary formulation of the theory. Renormalization of the model is discussed. A nonpower-counting renormalizable extension, obeying the defining functional identities of the theory, is presented. This extension is physically equivalent to the tree-level inclusion of a dimension-six effective operator [Formula: see text]. The resulting UV divergences are arranged in a perturbation series around the power-counting renormalizable theory. The application of the formalism to the Standard Model in the presence of the dimension-six operator [Formula: see text] is discussed.

Universal horizons in maximally symmetric spaces

Universal horizons in Hořava–Lifshitz gravity and Einstein-æther theory are the equivalent of causal horizons in general relativity and appear to have many of the same properties, including a first law of horizon thermodynamics and thermal radiation. Since universal horizons are infrared (IR) solutions of a putative power counting renormalizable quantum gravitational theory, fully understanding their thermodynamics will shed light on the interplay between black hole thermodynamics and quantum gravity. In this paper, we provide a complete classification, including asymptotic charges, of all four-dimensional static and spherically symmetric universal horizon solutions with maximally symmetric asymptotics — the equivalents of the Schwarzschild, Schwarzschild–de Sitter or Schwarzschild–anti-de Sitter spacetimes. Additionally, we derive the associated first laws for the universal horizon solutions. Finally, we prove that independent of asymptotic boundary conditions, any spherically symmetric solution in Hořava–Lifshitz gravity with a universal horizon is also a solution of Einstein-æther theory, thereby broadening and complementing the known equivalence region of the solution spaces.

Renormalization group equation for weakly power-counting renormalizable theories

We study the renormalization group flow in weak power counting (WPC) renormalizable theories. The latter are theories which, after being formulated in terms of certain variables, display only a finite number of independent divergent amplitudes order by order in the loop expansion. Using as a toolbox the well-known SU(2) non linear sigma model, we prove that for such theories a renormalization group equation holds that does not violate the WPC condition: that is, the sliding of the scale $\mu$ for physical amplitudes can be reabsorbed by a suitable set of finite counterterms arising at the loop order prescribed by the WPC itself. We explore in some detail the consequences of this result; in particular, we prove that it holds in the framework of a recently introduced beyond the Standard Model scenario in which one considers non-linear St\"uckelberg-like symmetry breaking contributions to the fermion and gauge boson mass generation mechanism.

Emergence of time in power-counting renormalizable Riemannian theory of gravity

We suggest a new scenario of gravitation in which gravity at the fundamental level is described by a Riemannian (i.e., locally Euclidean) theory without the notion of time. The Lorentzian metric structure and the notion of time emerge as effective properties at long distances. On the other hand, at short distances, higher derivative terms compatible with the Riemannian diffeomorphism become important and the system is described by a power-counting renormalizable Riemannian theory.

Hořava-Lifshitz gravity withλ→∞

In the framework of the power-counting renormalizable theory of gravitation, recently proposed by Ho\v{r}ava, we study the limit $\lambda\to\infty$, which is arguably the most natural candidate for the ultraviolet fixed point of the renormalization group flow. In the projectable version with dynamical critical exponent $z=3$, we analyze the Friedmann-Robertson-Walker background driven by the so-called "dark matter as integration constant" and perturbations around it. We show that amplitudes of quantum fluctuations for both scalar and tensor gravitons remain finite in the limit and that the theory is weakly coupled under a certain condition.

On-shell constructibility of tree amplitudes in general field theories

We study “on-shell constructibility” of tree amplitudes from recursion relations in general 4-dimensional local field theories with any type of particles, both massless and massive. Our analysis applies to renormalizable as well as non-renormalizable interactions, with or without supersymmetry. We focus on recursion relations that arise from complex deformations of all external momenta. Under certain conditions, these “all-line shift recursion relations” imply the MHV vertex expansion. We derive a simple sufficient criterion for the validity of the all-line shift recursion relations. It depends only on the mass dimensions of the coupling constants and on the sum of helicities of the external particles. Our proof is strikingly simple since it just relies on dimensional analysis and little-group transformation properties. In particular, the results demonstrate that all tree amplitudes with n > 4 external states are constructible in any power-counting renormalizable theory. Aspects of all-line shift constructibility are illustrated in numerous examples, ranging from pure scalar theory and the massless Wess-Zumino model to theories with higher-derivative interactions, gluon-Higgs fusion, and Z-boson scattering. We propose a sharp physical interpretation of our constructibility criterion: the all-line shift fails precisely for those classes of n-point amplitudes that can receive local contributions from independent gauge-invariant n-field operators.

Stability of the Einstein static universe in IR modified Hořava gravity

Recently, Hořava proposed a power counting renormalizable theory for (3+1)-dimensional quantum gravity, which reduces to Einstein gravity with a non-vanishing cosmological constant in IR, but possesses improved UV behaviors. In this work, we analyze the stability of the Einstein static universe by considering linear homogeneous perturbations in the context of an IR modification of Hořava gravity, which implies a ‘soft’ breaking of the ‘detailed balance’ condition. The stability regions of the Einstein static universe is parameterized by the linear equation of state parameter w=p/ρ and the parameters appearing in the Hořava theory, and it is shown that a large class of stable solutions exists in the respective parameter space.

Projectable Hořava–Lifshitz gravity in a nutshell

Approximately one year ago Hořava proposed a power-counting renormalizable theory of gravity which abandons local Lorentz invariance. The proposal has been received with growing interest and resulted in various different versions of Hořava-Lifshitz gravity theories, involving a colourful potpourri of new terminology. In this proceedings contribution we first motivate and briefly overview the various different approaches, clarifying their differences and similarities. We then focus on a model referred to as projectable Hořava–Lifshitz gravity and summarize the key results regarding its viability.

Quantum field theory, gravity and cosmology in a fractal universe

We propose a model for a power-counting renormalizable field theory living in a fractal spacetime. The action is Lorentz covariant and equipped with a Stieltjes measure. The system flows, even in a classical sense, from an ultraviolet regime where spacetime has Hausdorff dimension 2 to an infrared limit coinciding with a standard $D$-dimensional field theory. We discuss the properties of a scalar field model at classical and quantum level. Classically, the field lives on a fractal which exchanges energy-momentum with the bulk of integer topological dimension D. Although an observer experiences dissipation, the total energy-momentum is conserved. The field spectrum is a continuum of massive modes. The gravitational sector and Einstein equations are discussed in detail, also on cosmological backgrounds. We find ultraviolet cosmological solutions and comment on their implications for the early universe.

Renormalization of gauge theories in curved space-time

We consider the renormalization of general gauge theories on curved space-time background, with the main assumption being the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Batalin-Vilkovisky (BV) formalism one can show that the theory possesses gauge invariant and diffeomorphism invariant renormalizability at quantum level, up to an arbitrary order of the loop expansion. Starting from this point we discuss the locality of the counterterms and the general prescription for constructing the power-counting renormalizable theories on curved background.

Primordial magnetic field from noninflationary cosmic expansion in Hořava-Lifshitz gravity

The origin of large-scale magnetic field in the Universe is one of the greatest mysteries in modern cosmology. We present a new mechanism for generation of large-scale magnetic field, based on the power-counting renormalizable theory of gravitation recently proposed by Ho\ifmmode \check{r}\else \v{r}\fi{}ava. Contrary to the usual case in general relativity, the $U(1)$ gauge symmetry of a Maxwell action in this theory permits terms breaking conformal invariance in the ultraviolet. Moreover, for high frequency modes, the anisotropic scaling intrinsic to the theory inevitably makes the sound horizon far outside the Hubble horizon. Consequently, noninflationary cosmic expansion in the early Universe naturally generates superhorizon quantum fluctuations of the magnetic field. Specializing our consideration to the case with the dynamical critical exponent $z=3$, we show an explicit set of parameters for which (i) the amplitude of generated magnetic field is large enough as a seed for the dynamo mechanism; (ii) backreaction to the cosmic expansion is small enough; and (iii) the high-energy dispersion relation is consistent with the most recent observational limits from MAGIC and Fermi collaborations.

Renormalizable acausal theories of classical gravity coupled with interacting quantum fields

We prove the renormalizability of various theories of classical gravity coupled with interacting quantum fields. The models contain vertices with dimensionalities greater than 4, a finite number of matter operators and a finite or reduced number of independent couplings. An interesting class of models is obtained from ordinary power-counting renormalizable theories, letting the couplings depend on the scalar curvature R of spacetime. The divergences are removed without introducing higher derivative kinetic terms in the gravitational sector. The metric tensor has a non-trivial running, even if it is not quantized. The results are proved applying a certain map that converts classical instabilities, due to higher derivatives, into classical violations of causality, whose effects become observable at sufficiently high energies. We study acausal Einstein–Yang–Mills theory with an R-dependent gauge coupling in detail. We derive all-order formulae for the beta functions of the dimensionality-six gravitational vertices induced by renormalization, such as RRμνρσRμνρσ. Such beta functions are related to the trace-anomaly coefficients of the matter subsector.

Gauge-independent effective gauge fields

The problem of a gauge-independent definition of the effective gauge field is considered. The Slavnov identities corresponding to a system of interacting quantum gauge and classical matter fields, playing the role of a measuring device, are obtained. With their help, in the case of power-counting renormalizable theories, gauge independence of the effective device action is proved in the low-energy limit. This allows one to introduce a gauge-independent notion of the effective gauge field.