Symmetric Metric-Affine Gravity is a theory of gravity with an independent non-metric connection, and zero torsion. It can be thought of as ordinary metric gravity coupled to a rank-3 tensor Q, symmetric in one pair of indices. This field carries a spin-3 degree of freedom. We find that, in contrast to the totally symmetric case, it is possible to arrange the parameters in the Lagrangian, so that, at the linearized level, the spin-3 state, either alone or in combination with a spin-0 state, has a healthy propagation.

We calculate the scattering amplitude in the two dimensional CP (1) model in a regularization scheme independent way. When using cutoff regularization, a new Feynman rule from the path integral measure is required if one is to preserve the symmetry. The physical running of the coupling with renormalization scale arises from a UV finite Feynman integral in all schemes. We reproduce the usual result with asymptotic freedom, but the pathway to obtaining the beta function can be different in different schemes. The results can be extended to the O(N) model, for all N. We also comment on the way that this model evades the classic argument by Landau against asymptotic freedom in non-gauge theories.

The Starobinsky model was born in a cosmological scenario where conformally coupled matter quantum field fluctuations on the vacuum drive a non trivial semiclassical energy momentum tensor quadratic in curvature. The presence of an unstable de Sitter solution of the semiclassical Einstein equations contributed to spread the idea that the early universe could have experienced an inflationary epoch. Effective "R + R^2" models of gravity have later gained much attention since their predictions are in very good agreement with the measurements of CMB data and tensor to scalar ratio bounds. In this paper we observe how the Starobinsky model can be well approximated by the asymptotically free quadratic gravity on a part of a renormalization group trajectory (below some high UV scale) which is free from tachyonic instabilities, if a definition of “physical” running is employed.

We investigate symmetric Metric-Affine Theories of Gravity with a Lagrangian containing all operators of dimension up to four that are relevant to free propagation in flat space. Complementing recent work in the antisymmetric case, we derive the conditions for the existence of a single massive particle with good properties, in addition to the graviton.

It has been shown that if one solves self-consistently the semiclassical Einstein equations in the presence of a quantum scalar field, with a cutoff on the number of modes, spacetime become flatter when the cutoff increases. Here we extend the result to include the effect of fields with spin 0, 1/2, 1 and 2. With minor adjustments, the main result persists. Remarkably, one can have positive curvature even if the cosmological constant in the bare action is negative.

To deepen our understanding of Quantum Gravity and its connections with black holes and cosmology, building a common language and exchanging ideas across different approaches is crucial. The Nordita Program "Quantum Gravity: from gravitational effective field theories to ultraviolet complete approaches" created a platform for extensive discussions, aimed at pinpointing both common grounds and sources of disagreements, with the hope of generating ideas and driving progress in the field. This contribution summarizes the twelve topical discussions held during the program and collects individual thoughts of speakers and panelists on the future of the field in light of these discussions.

This book presents in a systematic fashion a number of quantum field theoretic phenomena that have a topological underpinning. The systematics is provided by the homotopy groups of the configuration space: solitons and instantons are related to the zeroth and first homotopy groups respectively, and quantized parameters to the second. The close relation of some of these notions to anomalies is also discussed. These concepts have many applications, from particle physics to statistical and condensed matter physics. The focus is mainly on the former, but some particularly instructive examples of the latter are also described.

We explore the properties of a simple renormalizable shift symmetric model with a higher derivative kinetic energy and quartic derivative coupling, that can serve as a toy model for higher derivative theories of gravity. The scattering amplitude behaves as in a normal effective field theory below the threshold for the production of ghosts, but has an unexpectedly soft behavior above the threshold. The physical running of the parameters is extracted from the 2-point and 4-point amplitudes. The results are compared to those obtained by other methods and are found to agree only in limiting cases. We draw several lessons that may apply also to gravity.

We argue that the well-known beta functions of quadratic gravity do not correspond to the physical dependence of scattering amplitudes on external momenta, and derive the correct physical beta functions. Asymptotic freedom turns out to be compatible with the absence of tachyons.

This collection of perspective pieces captures recent advancements and reflections from a dynamic research community dedicated to bridging quantum gravity, hydrodynamics, and emergent cosmology. It explores four key research areas: (a) the interplay between hydrodynamics and cosmology, including analog gravity systems; (b) phase transitions, continuum limits and emergent geometry in quantum gravity; (c) relational perspectives in gravity and quantum gravity; and (d) the emergence of cosmological models rooted in quantum gravity frameworks. Each contribution presents the distinct perspectives of its respective authors. Additionally, the introduction by the editors proposes an integrative view, suggesting how these thematic units could serve as foundational pillars for a novel theoretical cosmology framework termed "hydrodynamics on superspace".

We consider a quantum scalar field in a classical (Euclidean) De Sitter background, whose radius is fixed dynamically by Einstein's equations. In the case of a free scalar, it has been shown by Becker and Reuter that if one regulates the quantum effective action by putting a cutoff $N$ on the modes of the quantum field, the radius is driven dynamically to infinity when $N$ tends to infinity. We show that this result holds also in the case of a self-interacting scalar, both in the symmetric and broken-symmetry phase. Furthermore, when the gravitational background is put on shell, the quantum corrections to the mass and quartic self-coupling are found to be finite.

Abstract Poincaré Gauge Theories are a class of Metric-Affine Gravity theories with a metric-compatible (i.e. Lorentz) connection and with an action quadratic in curvature and torsion. We perform an explicit one-loop calculation starting with a single term of each type and show that not only are all other terms generated, but also many others. In our particular model all terms containing torsion are redundant and can be eliminated by field redefinitions, but there remains a new term quadratic in curvature, making the model non-renormalizable. We discuss the likely behavior of more general theories of this type.

Classical gravity is understood as the geometry of spacetime, and it seems very different from the other known interactions. In this review, I will instead stress the analogies: Like strong interactions, the low energy effective field theory of gravity is related to a nonlinearly realized symmetry, and like electroweak interactions, it is a gauge theory in Higgs phase, with a massive connection. I will also discuss the possibility of finding a UV complete quantum field theoretic description of all interactions.

A bstract A scalar theory can have many Gaussian (free) fixed points, corresponding to Lagrangians of the form ϕ □ n ϕ . We use the non-perturbative RG to study examples of flows between such fixed points. We show that the anomalous dimension changes continuously in such a way that at the endpoints the fields have the correct dimensions of the respective free theories. These models exhibit various pathologies, but are nonetheless interesting as examples of theories that are asymptotically free both in the infrared and in the ultraviolet. Furthermore, they illustrate the fact that a diverging coupling can actually correspond to a free theory.

We discuss theories of gravity with independent metric (or frame field) and connection, from the point of view of effective field theory. We count the parity-even Lagrangian terms of dimension up to four and give explicit bases for the independent terms that contribute to the two-point function. We then give the decomposition of the linearized action on a complete basis of spin projectors and consider various subclasses of Metric-Affine Gravity theories (MAGs). We show that teleparallel theories can be dynamically equivalent to any metric theory of gravity and give the particle content of those whose Lagrangian contains only dimension-two terms. We point out the existence of a class of MAGs whose EOMs do not admit propagating degrees of freedoms. Finally, we construct simple MAGs that contain only a massless graviton and a state of spin/parity $2^-$ or $3^-$. As a side result, we write the relativistic wave equation for a spin/parity $2^-$ state.

The non-perturbative functional renormalization group equation depends on the choice of a regulator function, whose main properties are a coarse-graining scale $k$ and an overall dimensionless amplitude $a$. In this paper we shall discuss the limit $a\to0$ with $k$ fixed. This limit is closely related to the pseudo-regulator that reproduces the beta functions of the $\overline{\text{MS}}\,$ scheme, that we studied in a previous paper. It is not suitable for precision calculations but it appears to be useful to eliminate the spurious breaking of symmetries by the regulator, both for nonlinear models and within the background field method.

The nonperturbative functional renormalization group equation depends on the choice of a regulator function, whose main properties are a "coarse-graining scale" k and an overall dimensionless amplitude a. In this paper we shall discuss the limit a -> 0 with k fixed. This limit is closely related to the pseudoregulator that reproduces the beta functions of the (MS) over bar scheme that we studied in a previous paper. It is not suitable for precision calculations but it appears to be useful to eliminate the spurious breaking of symmetries by the regulator, both for nonlinear models and within the background field method.

We construct a general effective dynamics for diffeomorphisms of spacetime, in a fixed external metric. Though related to familiar models of scalar fields as coordinates, our models have subtly different properties, both at kinematical and dynamical level. The energy–momentum (EM) tensor consists of two independently conserved parts. The background solution is the identity diffeomorphism and the EM tensor of this solution gives rise to an effective cosmological constant.

We formally prove the existence of a quantization procedure that makes the path integral of a general diffeomorphism-invariant theory of gravity, with fixed total spacetime volume, equivalent to that of its unimodular version. This is achieved by means of a partial gauge fixing of diffeomorphisms together with a careful definition of the unimodular measure. The statement holds also in the presence of matter. As an explicit example, we consider scalar-tensor theories and compute the corresponding logarithmic divergences in both settings. In spite of significant differences in the coupling of the scalar field to gravity, the results are equivalent for all couplings, including non-minimal ones.

We review various classical unified theories of gravity and other interactions that have appeared in the literature, paying special attention to scenarios in which spacetime remains four-dimensional, while an “internal” space is enlarged. The starting point for each such unification scenario is a particular formalism for General Relativity. We thus start by reviewing, besides the usual EinsteinHilbert and Palatini formulations, the Einstein-Cartan, MacDowell-Mansouri and BF (both nonchiral and chiral) formulations. Each of these introduces some version of “internal” bundle and a dynamical variable that ties the internal and tangent bundles. In each of these formulations there is also an independent connection in the “internal” bundle. One can then study the effects of “enlarging the internal space”, which typically leads to a theory of gravity and Yang-Mills fields. We review what has been done in the literature on each of these unification schemes, and compare and contrast their achievements to those of the better developed Kaluza-Klein scenario. Electronic address: kirill.krasnov@nottingham.ac.uk Electronic address: percacci@sissa.it