Roberto Percacci

A bstract: 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.

General Relativity and Yang-Mills theories are the two pillars of our understanding of the physical world. The fact that the former is a classical field theory whereas the latter are usually presented as quantum field theories, tends to obscure the similarities between them and is often given as a motivation to develop a quantum theory of gravity. In this book we instead treat both as classical theories, putting them on a more even basis. Insisting that the dynamical variables must have a global geometrical meaning exposes their deep common foundations and allows to give precise answers to otherwise vague questions such as whether gravity is a gauge theory. The book contains standard presentations of Yang-Mills theories and General Relativity but covers also several topics that are not very well known, such as the geometry of the Higgs phenomenon, the transformation of spinors under diffeomorphisms, the derivation of General Relativity from the principles of special relativistic field theory.

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.

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.

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.

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.

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.