<p>Asymptotic safety constitutes a promising mechanism for a consistent and predictive high-energy completion of the gravitational interactions. To date, most results on the interacting renormalization group fixed point underlying the construction are obtained for Euclidean signature spacetimes. In this work, we use the Arnowitt-Deser-Misner decomposition of the metric degrees of freedom and investigate the relations between the Euclidean and Lorentzian renormalization group flows resulting from the analytic continuation of the lapse function. We discuss the general conditions that guarantee the equivalence of the beta functions. These insights are illustrated based on the flow of the graviton two-point function within the Einstein-Hilbert truncation, demonstrating agreement of the Euclidean and Lorentzian settings. Hence, the UV and IR completions identified in the Euclidean case are robust when changing the spacetime signature. We take this as an important indicator that the Euclidean asymptotic safety mechanism carries over to Lorentzian signature spacetimes.</p>

Netherlands

Frank Saueressig

China

Jian Wang

Foliated asymptotically safe gravity: Lorentzian signature fluctuations from the Wick rotation

<p>The gravitational asymptotic safety program envisions the high-energy completion of gravity through an interacting renormalization group fixed point, the Reuter fixed point. The predictive power of the construction is encoded in the spectrum of the stability matrix which is obtained from linearizing the renormalization group flow around this fixed point. A key result of the asymptotic safety program is that parts of this spectrum exhibit an almost-Gaussian scaling behavior, entailing that operators which are classically highly UV irrelevant do not induce new free parameters. In this article, we track down the origin of this property by contrasting the structure of the stability matrix computed from the Wetterich equation and the composite-operator equation within the realm of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi><mo stretchy="false">(</mo><mi>R</mi><mo stretchy="false">)</mo></math> truncations. We show that the almost-Gaussian scaling is not linked to the classical part of the beta functions. It is a quantum-induced almost-Gaussian scaling originating from the quantum corrections in the flow equation. It relies on a subtle interplay among the analytic structure of the theory’s two-point function and the way the Wetterich equation integrates out fluctuation modes. As a byproduct we determine the parts of the eigenmode spectrum that is robust with respect to changing the regularization procedure.</p>

Maximilian Becker

Russia

Alexander Kurov

Remarks on the origin of almost-Gaussian scaling in asymptotically safe quantum gravity

Asymptotic safety is a powerful mechanism for obtaining a consistent and predictive quantum field theory beyond the realm of perturbation theory. It hinges on an interacting fixed point of the Wilsonian renormalization group flow which controls the microscopic dynamics. Connecting the fixed point to observations requires constructing the set of effective actions compatible with this microscopic dynamics. Technically, this information is stored in the UV-critical surface of the fixed point. In this work, we describe a novel approach for extracting this information based on analytical and pseudospectral methods. Our construction is illustrated at the level of the three-dimensional Ising model and easily generalizes to any asymptotically safe quantum field theory. It also constitutes an important step toward setting up a well-founded swampland program within the gravitational asymptotic safety program.

Agustín Silva

Harvesting physical predictions from asymptotically safe quantum field theories

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.

Mathijs Fraaije

Canada

Alessia Platania

On the reconstruction problem in quantum gravity

Asymptotic safety is a promising mechanism for obtaining a consistent and predictive quantum theory for gravity. The ADM formalism allows to introduce a (Euclidean) time-direction in this framework. It equips spacetime with a foliation structure by encoding the gravitational degrees of freedom in a lapse function, shift vector, and a metric measuring distances on the spatial slices. We use the Wetterich equation to study the renormalization group flow of the graviton 2-point function extracted from the spatial metric. The flow is driven by the 3- and 4-point vertices generated by the foliated Einstein-Hilbert action supplemented by minimally coupled scalar and vector fields. We derive bounds on the number of matter fields cast by asymptotic safety. Moreover, we show that the phase diagram obtained in the pure gravity case is qualitatively stable within these bounds. An intriguing feature is the presence of an IR-fixed point for the graviton mass which prevents the squared mass taking negative values. This feature persists for any number of matter fields and, in particular, also in situations where there is no suitable interacting fixed point rendering the theory asymptotically safe. Our work complements earlier studies of the subject by taking contributions from the matter fields into account.

Guus Korver

Global flows of foliated gravity-matter systems

The gravitational asymptotic safety program envisions a high-energy completion of gravity based on a non-Gaussian renormalization group fixed point. A key step in this program is the transition from Euclidean to Lorentzian signature spacetimes. One way to address this challenge is to formulate the quantum theory based on the Arnowitt-Deser-Misner decomposition of the metric field. This equips the Euclidean spacetime with a preferred direction which may serve as the time-direction in the Lorentzian setting. In this work we use the Wetterich equation in order to compute the renormalization group flow of the graviton two-point function. The resulting beta functions possess a non-Gaussian renormalization group fixed point suitable for rendering the theory asymptotically safe. The phase diagram underlying the flow of the two-point function is governed by the interplay between this non-Gaussian fixed point, the Gaussian fixed point, and an infrared fixed point. The latter ensures that the renormalized squared graviton mass cannot take negative values. These results are in qualitative agreement with fluctuation computations carried out in the covariant setting. We take this as non-trivial evidence that the asymptotic safety mechanism remains intact when considering quantum gravity on spacetimes carrying a foliation structure. Technically, our work constitutes the first fluctuation computation carried out within the ADM-framework. Therefore, we also provide a detailed discussion of the conceptual framework, highlighting the elements which differ from fluctuation computations in the covariant setting.

Foliated asymptotically safe gravity in the fluctuation approach

Wetterich's equation provides a powerful tool for investigating the existence and universal properties of renormalization group fixed points exhibiting quantum scale invariance. Motivated by recent works on asymptotically safe scalar-tensor theories, we develop a novel approximation scheme which projects the functional renormalization group equation onto functions of the kinetic term. Applying this projection to scalars and gauge fields, our analysis identifies a new universality class with a very special spectrum of stability coefficients. The implications of our findings in the context of asymptotically safe gravity-matter systems are discussed.

Cristobal Laporte

Nora Locht

Brazil

Antonio D. Pereira

Evidence for a novel shift-symmetric universality class from the functional renormalization group

A intriguing feature shared by many quantum gravity programs is the dynamical decrease of the spectral dimension from <math><msub><mi>D</mi><mi>s</mi></msub><mo>=</mo><mn>4</mn></math> at macroscopic to <math><msub><mi>D</mi><mi>s</mi></msub><mo>≈</mo><mn>2</mn></math> at microscopic scales. In this note, we study the impact of this transition on the energy loss of static, spherically symmetric black holes due to Hawking radiation. We demonstrate that the decrease in the spectral dimension renders the luminosity of a black hole finite. While this slightly increases the lifetime of light black holes, we find that this mechanism is insufficient to generate long-lived black hole remnants. We briefly comment on the relation of our findings to previous work on this topic.

Amir Khosravi

Black hole remnants from dynamical dimensional reduction?

Asymptotic Safety provides an elegant mechanism for obtaining a consistent high-energy completion of gravity and gravity-matter systems. Following the initial idea by Steven Weinberg, the construction builds on an interacting fixed point of the theories renormalization group (RG) flow. In this work we use the Wetterich equation for the effective average action to investigate the RG flow of gravity supplemented by a real scalar field. We give a non-perturbative proof that the subspace of interactions respecting the global shift-symmetry of the scalar kinetic term is closed under RG transformations. Subsequently, we compute the beta functions in an approximation comprising the Einstein-Hilbert action supplemented by the shift-symmetric quartic scalar self-interaction and the two lowest order shift-symmetric interactions coupling scalar-bilinears to the spacetime curvature. The computation utilizes the background field method with an arbitrary background, demonstrating that the results are manifestly background independent. Our beta functions exhibit an interacting fixed point suitable for Asymptotic Safety, where all matter interactions are non-vanishing. The presence of this fixed point is rooted in the interplay of the matter couplings which our work tracks for the first time. The relation of our findings with previous results in the literature is discussed in detail and we conclude with a brief outlook on potential phenomenological applications.

Antonio Pereira

Scalar-tensor theories within Asymptotic Safety

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.