Ultralight scalar dark matter may couple to the Standard Model through dimension-five operators that contain the field-strength tensors of the gauge interactions. Recent progress in nuclear clocks is projected to increase the sensitivity to such couplings by several orders of magnitude. Future experimental constraints may even have Planck-scale sensitivity, calling for a study of such couplings in a framework that includes quantum gravity. We take a first step towards providing the theoretical constraints on such couplings that arise in asymptotically safe gravity. We find evidence that such couplings vanish in asymptotically safe gravity and are also not generated in a perturbative quantum-gravity regime that describes quantum gravity as an effective field theory.

Germany

United Kingdom

Gabriel Assant

Astrid Eichhorn

Benjamin Knorr

Towards theory constraints on ultralight dark matter from quantum gravity

<p>We analyze the renormalization group flow of quantum gravity at sixth order in the derivative expansion within the background field approximation. Nonlinear field redefinitions are used to ensure that only essential couplings flow. Working within the universality class of general relativity, with a vanishing cosmological constant, redundant couplings are fixed to their values at the Gaussian fixed point. This reduces the theory space to two dynamical essential couplings given by Newton’s and the Goroff-Sagnotti coupling. Furthermore, it implements the condition that no extra degrees of freedom are present beyond those of general relativity, in contrast to higher derivative theories and derivative expansions in a conventional renormalization scheme. We find a unique ultraviolet fixed point with a single relevant direction and analyze the phase diagram of the theory. Our results suggest resilience of the gravitational Reuter fixed point under the inclusion of higher order curvature invariants and show several signs of near perturbativity. The regulator dependence of our results is investigated in detail and shows that qualitative and quantitative features are robust to a large extent.</p>

Italy

Alessio Baldazzi

Uruguay

Kevin Falls

Canada

Yannick Kluth

Robustness of the derivative expansion in asymptotic safety

We compute the asymptotic safety landscape stemming from ultraviolet-complete photon-graviton flows in a field theoretic setup, and we confront it with the weak gravity conjecture and, for the first time, with positivity bounds. At fourth order in derivatives, we find two gravitational fixed points providing viable ultraviolet completions for the theory. One of them comes with a single relevant direction, which sets the scale of quantum gravity. The corresponding sub-landscape is a single point. The second fixed point yields a richer sub-landscape of effective theories, most of which is described by an approximately straight line in the space of dimensionless Wilson coefficients. We additionally discover that: the two sub-landscapes are continuously connected via a small “candy cane” regime, and the whole asymptotic safety landscape falls onto a plane; this is consistent with earlier findings and could be a universal feature in Asymptotic Safety; in such a field-theoretic setup, the Euler coupling plays a special role, as it is unconstrained by quantum scale invariance, but can enter off-shell bounds such as entropy-based positivity constraints; Planck-scale-suppressed violations of both weak gravity and positivity bounds occur across the landscape. The latter result resonates with expectations grounded on effective field theory arguments.

Denmark

Alessia Platania

Unearthing the intersections: positivity bounds, weak gravity conjecture, and asymptotic safety landscapes from photon-graviton flows

We discuss general momentum-dependent field redefinitions in the context of quantum-gravitational scattering amplitudes in general, and asymptotic safety in particular. Implementing such redefinitions at the lowest curvature order, we can bring the graviton propagator into tree-level form, avoiding issues of fiducial ghost poles and their associated violations of unitarity. We compute the beta function for Newton’s constant, and find an asymptotically safe fixed point whose critical exponent changes by 0.4% compared to not resolving the momentum-dependent field redefinition. This provides a strong indication that this fixed point does not feature extra degrees of freedom related to ghostly modes, and has a good chance of being related to a unitary theory.

Sweden

Momentum-dependent field redefinitions in asymptotic safety

The weak-gravity bound has been discovered in several asymptotically safe gravity-matter systems. It limits the strength of gravitational fluctuations that are compatible with an ultraviolet-complete matter sector and results from the collision of two partial fixed points of the matter system as a function of the strength of the gravitational interactions. In this paper, we will investigate this mechanism in detail for a shift-symmetric scalar field. First, we will study the fixed point structure of the scalar system without gravity. We find indications that the Gaussian fixed point is the only viable fixed point, suggesting that a weak-gravity bound resulting from the collision of two partial fixed points is a truncation artifact. We will then couple the scalar system to gravity and perform different expansions to track the Gaussian fixed point as gravitational fluctuations become stronger. We also introduce a new notion of the weak-gravity bound that is based on the number of relevant operators.

Gustavo P. de Brito

Marc Schiffer

On the weak-gravity bound for a shift-symmetric scalar field

We discuss some aspects of the metric configuration space in quantum gravity in the background field formalism. We give a necessary and sufficient condition for the parametrization of Euclidean metric fluctuations such that (i) the signature of the metric is preserved in all configurations that enter the gravitational path integral, and (ii) the parametrization provides a bijective map between full Euclidean metrics and metric fluctuations about a fixed background. For the case of foliatable manifolds, we show how to parametrize fluctuations in order to preserve foliatability of all configurations. Moreover, we show explicitly that preserving the signature on the configuration space for the Lorentzian quantum gravitational path integral is most conveniently achieved by inequality constraints. We discuss the implementation of these inequality constraints in a nonperturbative renormalization group setup.

Configuration space for quantum gravity in a locally regularized path integral

We tackle the question of whether regular black holes or other alternatives to the Schwarzschild solution can arise from an action principle in quantum gravity. Focusing on an asymptotic expansion of such solutions and inspecting the corresponding field equations, we demonstrate that their realization within a principle of stationary action would require either fine-tuning, or strong infrared nonlocalities in the gravitational effective action. This points to an incompatibility between large-distance locality and many of the proposed alternatives to classical black holes.

Sifting quantum black holes through the principle of least action

We present the complete set of universal one-loop beta functions of cubic gravity in six dimensions. The system admits over 8000 distinct fixed points, of which more than 200 are real. Some of them might be relevant for the quantization of gravity in the physical case of four dimensions.

One-Loop Renormalization of Cubic Gravity in Six Dimensions

Affine gravity is a connection-based formulation of gravity that does not involve a metric. After a review of basic properties of affine gravity, we compute the tree-level scattering amplitude of scalar particles interacting gravitationally via the connection in a curved spacetime. We find that, while classically equivalent to general relativity, affine gravity differs from metric quantum gravity.

Chris Ripken

Scattering amplitudes in affine gravity

We employ the curvature expansion of the quantum effective action for gravity-matter systems to construct graviton-mediated scattering amplitudes for non-minimally coupled scalar fields in a Minkowski background. By design, the formalism parameterises all quantum corrections to these processes and is manifestly gauge-invariant. The conditions resulting from UV-finiteness, unitarity, and causality are analysed in detail and it is shown by explicit construction that the quantum effective action provides sufficient room to meet these structural requirements without introducing non-localities or higher-spin degrees of freedom. Our framework provides a bottom-up approach to all quantum gravity programs seeking for the quantisation of gravity within the framework of quantum field theory. Its scope is illustrated by specific examples, including effective field theory, Stelle gravity, infinite derivative gravity, and Asymptotic Safety.