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.

Germany

Benjamin Knorr

Denmark

Alessia Platania

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

Local higher-derivative corrections to the Einstein-Hilbert action yield sub-leading corrections to the Bekenstein-Hawking area law. Here we show that if the quantum effective action comprises a certain class of infrared non-localities, the entropy of large black holes generally diverges to either positive or negative infinity. In such theories, large spherically symmetric black holes would be either highly chaotic or thermodynamically impossible, respectively. In turn, this puts strong constraints on the Laurent expansion of the form factors in the effective action.

Canada

Sweden

Jaime Redondo–Yuste

Diverging black hole entropy from quantum infrared non-localities

Path integrals and the Wilsonian renormalization group provide two complementary computational tools for investigating continuum approaches to quantum gravity. The starting points of these constructions utilize a bare action and a fixed point of the renormalization group flow, respectively. While it is clear that there should be a connection between these ingredients, their relation is far from trivial. This results in the so-called reconstruction problem. In this work, we demonstrate that the map between these two formulations does not generate non-localities at quadratic order in the background curvature. At this level, the bare action in the path integral and the fixed-point action obtained from the Wilsonian renormalization group differ by local terms only. This conclusion does not apply to theories coming with a physical ultraviolet cutoff or a fundamental non-locality scale.

Netherlands

Mathijs Fraaije

Frank Saueressig

On the reconstruction problem in quantum gravity

We propose a new method to account for quantum-gravitational effects in cosmological and black hole spacetimes. At the core of our construction is the “decoupling mechanism”: when a physical infrared scale overcomes the effect of the regulator implementing the Wilsonian integration of fluctuating modes, the renormalization group flow of the scale-dependent effective action freezes out, so that at the decoupling scale the latter approximates the standard quantum effective action. Identifying the decoupling scale allows to access terms in the effective action that were not part of the original truncation and thus to study leading-order quantum corrections to field equations and their solutions. Starting from the Einstein-Hilbert truncation, we exploit for the first time the decoupling mechanism in quantum gravity to investigate the dynamics of quantum-corrected black holes from formation to evaporation. Our findings are in qualitative agreement with previous results in the context of renormalization group improved black holes, but additionally feature novel properties reminiscent of higher-derivative operators with specific non-local form factors.

Johanna Borissova

Formation and evaporation of quantum black holes from the decoupling mechanism in quantum gravity

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.

Marc Schiffer

Configuration space for quantum gravity in a locally regularized path integral

Resumming quantum fluctuations at the level of the gravitational path integral is expected to result in non-local effective actions and thus in a non-trivial momentum dependence of the propagator. Which properties the (dressed) graviton propagator has to satisfy and whether they can all be met are key open questions. In this work we present criteria and conditions for the momentum dependence of a graviton propagator which is consistent with unitarity, causality, and stability in a non-perturbative setting. To this end, we revisit several aspects of these conditions, highlighting some caveats and subtleties that got lost in recent discussions, and spelling out others that to our best knowledge have not been studied in detail. We discuss the consequences of these concepts for the properties of the graviton propagator. Finally, we provide examples of propagators satisfying unitarity and causality, while avoiding tachyonic and vacuum instabilities, and allowing for an analytic Wick rotation.

Causality, unitarity and stability in quantum gravity: a non-perturbative perspective

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

Higher-derivative corrections to cosmological effective actions in string theory are largely constrained by T-duality, but have been computed hitherto only to the first few orders in the string scale <math><msup><mi>α</mi><mo>′</mo></msup></math>. The functional renormalization group, in conjunction with the strong constraints imposed by T-duality, allows us to derive cosmological effective actions to all orders in <math><msup><mi>α</mi><mo>′</mo></msup></math> while avoiding “truncations” of the theory space. We show that the resulting higher-derivative <math><msup><mi>α</mi><mo>′</mo></msup></math>-corrections forbid the existence of de Sitter vacua, at least in regimes where string-loop corrections can be neglected. Our findings thus support the no-de Sitter swampland conjecture in the presence of all-order effects in <math><msup><mi>α</mi><mo>′</mo></msup></math>.

Belgium

Ivano Basile

String tension between de Sitter vacua and curvature corrections

We employ the techniques of the Functional Renormalization Group in string theory, in order to derive an effective mini-superspace action for cosmological backgrounds to all orders in the string scale α′. To this end, T-duality plays a crucial role, classifying all perturbative curvature corrections in terms of a single function of the Hubble parameter. The resulting renormalization group equations admit an exact, albeit non-analytic, solution in any spacetime dimension D, which is however incompatible with Einstein gravity at low energies. Within an E-expansion about D = 2, we also find an analytic solution which exhibits a non-Gaussian ultraviolet fixed point with positive Newton coupling, as well as an acceptable low-energy limit. Yet, within polynomial truncations of the full theory space, we find no evidence for an analog of this solution in D = 4. Finally, we comment on potential cosmological implications of our findings.

Cosmological α′-corrections from the functional renormalization group

We discuss aspects of non-perturbative unitarity in quantum field theory. The additional ghost degrees of freedom arising in “truncations” of an effective action at a finite order in derivatives could be fictitious degrees of freedom. Their contributions to the fully-dressed propagator – the residues of the corresponding ghost-like poles – vanish once all operators compatible with the symmetry of the theory are included in the effective action. These “fake ghosts” do not indicate a violation of unitarity.