We study the consistency of Scalar Gauss-Bonnet Gravity, a generalization of General Relativity where black holes can develop non-trivial hair by the action of a coupling F(Φ)  <math> <mi>G</mi> </math>  $$ \mathcal{G} $$  between a function of a scalar field and the Gauss-Bonnet invariant of the space-time. When properly normalized, interactions induced by this term are weighted by a cut-off, and take the form of an Effective Field Theory expansion. By invoking the existence of a Lorentz invariant, causal, local, and unitary UV completion of the theory, we derive positivity bounds for n-to-n scattering amplitudes including exchange of dynamical gravitons. These constrain the value of all even derivatives of the function F(Φ), and are highly restrictive. They require some of the scales of the theory to be of Planckian order, and rule out most of the models used in the literature for black hole scalarization.

Italy

Mario Herrero-Valea

The shape of scalar Gauss-Bonnet gravity

We formulate positivity bounds for scattering amplitudes including exchange of massless particles. We generalize the standard construction through dispersion relations to include the presence of a branch cut along the real axis in the complex plane for the Maldestam variable <math><mi>s</mi></math>. In general, validity of these bounds requires the cancellation of divergences in the forward limit of the amplitude, proportional to <math><msup><mi>t</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> and <math><mi>log</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>. We show that this is possible in the case of gravitons if one assumes a Regge behavior of the amplitude at high energies below the Planck scale, as previously suggested in the literature, and that the concrete UV behavior of the amplitude is uniquely determined by the structure of IR divergences. We thus extend previous results by including a subleading logarithmic term, which we show to be universal. The bounds that we present here have the potential of constraining very general models of modified gravity and effective field theories of matter coupled to gravitation.

Spain

Raquel Santos-Garcia

Finland

Russia

Anna Tokareva

Massless positivity in graviton exchange

The persistence of a suitable notion of black hole thermodynamics in Lorentz breaking theories of gravity is not only a non-trivial consistency test for such theories, it is also an interesting investigation per se, as it might help us identifying the crucial features at the root of these surprising laws governing such purely gravitational objects. In past investigations, controversial findings were presented in this sense. With the aim of settling this issue, we present here two complementary derivations of Hawking radiation in geometries endowed with universal horizons: a novel feature of back holes in Lorentz breaking theories of gravity which reproduces several properties normally characterizing Killing horizons. We find that both the derivations agree on the fact that the Hawking temperature associated to these geometries is set by the generalized universal horizon peeling surface gravity, as required for consistency with extant derivations of the first law of thermodynamics for these black holes. We shall also comment on the compatibility of our results with previous alternative derivations and on their significance for the survival of the generalized second law of black hole thermodynamics in Lorentz breaking theories of gravity.

Stefano Liberati

Hawking radiation from universal horizons

Unimodular Gravity is normally assumed to be equivalent to General Relativity for all matters but the character of the Cosmological Constant. Here we discuss this equivalence in the presence of a non-minimally coupled scalar field. We show that when we consider gravitation to be dynamical in a QFT sense, quantum corrections can distinguish both theories if the non-minimal coupling is non-vanishing. In order to show this, we construct a path integral formulation of Unimodular Gravity, fixing the complicated gauge invariance of the theory and computing all one-loop divergences. We find a combination of the couplings in the Lagrangian to which we can assign a physical meaning. It tells whether quantum gravitational phenomena can be ignored or not at a given energy scale. Its renormalization group flow differs depending on if it is computed in General Relativity or Unimodular Gravity.

Non-minimal tinges of Unimodular Gravity

We revisit the question of frame equivalence in Quantum Field Theory in the presence of gravity, a situation of relevance for theories aiming to describe the early Universe dynamics and Inflation in particular. We show that in those cases, the path integral measure must be carefully defined and that the requirement of diffeomorphism invariance forces it to depend non-trivially on the fields. As a consequence, the measure will transform also non-trivially between different frames and it will induce a new finite contribution to the Quantum Effective Action that we name frame discriminant. This new contribution must be taken into account in order to assess the dynamics and physical consequences of a given theory. We apply our result to scalar-tensor theories described in the Einstein and Jordan frame, where we find that the frame discriminant can be thought as inducing a scale-invariant regularization scheme in the Jordan frame.

Kevin Falls

Switzerland

Frame (in)equivalence in quantum field theory and cosmology

We compute the renormalization group running of the Newton constant and the parameter <math><mi>λ</mi></math> in (<math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional projectable Hořava gravity. We use the background-field method, expanding around configurations with flat spatial metric, but nonvanishing shift. This allows us to reduce the number of interaction vertices and thereby drastically simplify the calculations. The gauge-invariant <math><mi>β</mi></math>-function of <math><mi>λ</mi></math> has two families of zeros, attractive in the infrared and ultraviolet, respectively. They are candidates for the fixed points of the full renormalization group flow of the theory, once the <math><mi>β</mi></math>-functions for the rest of the couplings are added.

Andrei O. Barvinsky

CERN

Sergey M. Sibiryakov

Towards the renormalization group flow of Hořava gravity in <math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math> dimensions

We revisit the problem of constraining the weak field limit of the gravitational lagrangian from S-matrix properties. From unitarity and Lorentz invariance of the S-matrix of massless gravitons, we derive on-shell gauge invariance to consist on the transverse part of the linearised diffeomorphisms group. Moreover, by looking to the interaction between sources, we conclude that there exist only two possible lagrangians that lead to a welldefined covariant interaction, corresponding to the weak field limits of General Relativity and Unimodular Gravity. Additionally, this result confirms the equivalence of the S-matrix of both theories around flat space-time.

What do gravitons say about (unimodular) gravity?

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 Hořava 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.

Andrei Barvinsky

Diego Blas

Sergey Sibiryakov

Germany

Christian Steinwachs

Renormalization of gauge theories in the background-field approach

We present a new color decomposition for QCD amplitudes at one-loop level as a generalization of the Del Duca-Dixon-Maltoni and Johansson-Ochirov decomposition at tree level. Starting from a minimal basis of planar primitive amplitudes we write down a color decomposition that is free of linear dependencies among appearing primitive amplitudes or color factors. The conjectured decomposition applies to any number of quark flavors and is independent of the choice of gauge group and matter representation. The results also hold for higher-dimensional or supersymmetric extensions of QCD. We provide expressions for any number of external quark-antiquark pairs and gluons.

Sweden

Gregor Kälin

Cyclic Mario worlds — color-decomposition for one-loop QCD

We study the one-loop covariant effective action of Lifshitz theories using the heat kernel technique. The characteristic feature of Lifshitz theories is an anisotropic scaling between space and time. This is enforced by the existence of a preferred foliation of space-time, which breaks Lorentz invariance. In contrast to the relativistic case, covariant Lifshitz theories are only invariant under diffeomorphisms preserving the foliation structure. We develop a systematic method to reduce the calculation of the effective action for a generic Lifshitz operator to an algorithm acting on known results for relativistic operators. In addition, we present techniques that drastically simplify the calculation for operators with special properties. We demonstrate the efficiency of these methods by explicit applications.