arXiv subjects

Gian Paolo Vacca

Publications and source records attributed to Gian Paolo Vacca.

At least 19 recordsLinked to original sources

arXiv2026

Proper-time functional renormalization in $O(N)$ scalar models coupled to gravity

We focus on the use of the functional Wilsonian renormalization group framework characterized by a proper time regulator and test its use in the search of the scaling solutions and the critical properties of an O(N)-invariant scalar field multiplet coupled to gravity in d=4 and d=3 dimensions. We employ the same background-fluctuation splitting and gauge fixing procedure, already adopted in a previous study based, instead, on the effective average action framework and a similar truncation of the effective action. Our main goal is to compare the results for the scaling solutions and some of the associated critical exponents. In this analysis, performed in a different framework, most of the picture previously uncovered is confirmed both at qualitative and quantitative level. There are, neverthelss, few differences both at finite N and in its large value limit, depending also on the schemes which in both frameworks are called 'improved'

hep-th↗

arXiv2025

The Starobinsky model of inflation and Renormalizability

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.

hep-th↗

arXiv2024

Substructures of the Weyl group and their physical applications

We study substructures of the Weyl group of conformal transformations of the metric of (pseudo)Riemannian manifolds. These substructures are identified by differential constraints on the conformal factors of the transformations which are chosen such that their composition is associative. Mathematically, apart from rare exceptions, they are partial associative groupoids, not groups, so they do not have an algebra of infinitesimal transformations, but this limitation can be partially circumvented using some of their properties cleverly. We classify and discuss the substructures with two-derivatives differential constraints, the most famous of which being known as the harmonic or restricted Weyl group in the physics literature, but we also show the existence of a lightcone constraint which realizes a proper subgroup of the Weyl group. We then show the physical implications that come from invariance under the two most important substructures, concentrating on classical properties of the energy-momentum tensor and a generalization of the quantum trace anomaly. We also elaborate further on the harmonic substructure, which can be interpreted as partial gauge fixing of full Weyl invariance using BRST methods. Finally, we discuss how to construct differential constraints of arbitrary higher-derivative order and present, as examples, generalizations involving scalar constraints with four and six derivatives.

hep-th↗

arXiv2024

Emergent symmetries at criticality in multi field RFT/DP

We study multifield extensions of Reggeon Field Theory (also equivalent to Directed Percolation model) at criticality in the perturbative epsilon-expansion below the upper critical dimension Dc=4 at one loop, for the special case when all fields have the same scale (anomalous) dimensions. Analyzing all the fixed points of the renormalization group flow for N=2 flavors and some for N=3, we find scale invariant solutions which are characterized by specific emergent global symmetries of the interacting potential. We also study two infinite families as a function of N having Z_N and S_{N+1} symmetries.

hep-th↗

arXiv2022

Perturbative approaches to non-perturbative quantum gravity

We discuss the birth of the non-perturbative approach to quantum gravity known as quantum Einstein gravity, in which the gravitational interactions are conjectured to be asymptotically safe. The interactions are assumed to be finite and consistent at high energies thanks to a scale-invariant ultraviolet completion. We present the framework on the basis of perturbative arguments that originally motivated it, paying special attention to the $ε$-expansion in $d=2+ε$ dimensions and the large-$N$ expansion for $N$ the number of flavors of matter fields. The chapter is organized in such a way that each section is mostly independent and can offer several ideas for both conceptual and technical future developments.

hep-th↗

arXiv2022

Weyl Covariance and the Energy Momentum Tensors of Higher-Derivative Free Conformal Field Theories

Energy momentum tensors of higher-derivative free scalar conformal field theories in flat spacetime are discussed. Two algorithms for the computation of energy momentum tensors are described, which accomplish different goals: the first is brute-force and highlights the complexity of the energy momentum tensors, while the second displays some features of their geometric origin as variations of Weyl invariant curved-space actions. New compact expressions for energy momentum tensors are given and specific obstructions to defining them as conformal primary operators in some spacetime dimensions are highlighted. Our discussion is also extended to higher-derivative free spinor theories, which are based on higher-derivative generalizations of the Dirac action and provide interesting examples of conformal field theories in dimension higher than two.

hep-th↗

arXiv2022

Scale and Conformal Invariance in Higher Derivative Shift Symmetric Theories

The critical behavior of infinite families of shift symmetric interacting theories with higher derivative kinetic terms (non unitary) is considered. Single scalar theories with shift symmetry are classified according to their upper critical dimensions and studied at the leading non trivial order in perturbation theory. For two infinite families, one with quartic and one with cubic interactions, beta functions, criticality conditions and universal anomalous dimensions are computed. At the order considered, the cubic theories enjoy a one loop non renormalization of the vertex, so that the beta function depends non trivially only on the anomalous dimension. The trace of the energy momentum tensor is also investigated and it is shown that these two families of QFTs are conformally invariant at the fixed point of the RG flow.

hep-th↗

arXiv2021

A Fake Instability in String Inflation

In type IIB Fibre Inflation models the inflaton is a Kaehler modulus which is kinetically coupled to the corresponding axion. In this setup the curvature of the field space induces tachyonic isocurvature perturbations normal to the background inflationary trajectory. However we argue that the associated instability is unphysical since it is due to the use of ill-defined entropy variables. In fact, upon using the correct relative entropy perturbation, we show that in Fibre Inflation axionic isocurvature perturbations decay during inflation and the dynamics is essentially single-field.

hep-th↗

arXiv2021

On the choice of entropy variables in multifield inflation

We discuss the usefulness and theoretical consistency of different entropy variables used in the literature to describe isocurvature perturbations in multifield inflationary models with a generic curved field space. We clarify which is the proper entropy variable to be used to match the evolution of isocurvature modes during inflation to the one after the reheating epoch in order to compare with observational constraints. In particular, we find that commonly used variables, as the relative entropy perturbation or the one associated to the decomposition in tangent and normal perturbations with respect to the inflationary trajectory, even if more useful to perform numerical studies, can lead to results which are wrong by several orders of magnitude, or even to apparent destabilisation effects which are unphysical for cases with light kinetically coupled spectator fields.

astro-ph.CO↗

arXiv2020

A multicritical Landau-Potts field theory

We investigate a perturbatively renormalizable $S_{q}$ invariant model with $N=q-1$ scalar field components below the upper critical dimension $d_c=\frac{10}{3}$. Our results hint at the existence of multicritical generalizations of the critical models of spanning random clusters and percolations in three dimensions. We also discuss the role of our multicritical model in a conjecture that involves the separation of first and second order phases in the $(d,q)$ diagram of the Potts model.

cond-mat.stat-mech↗

arXiv2020

Crossover exponents, fractal dimensions and logarithms in Landau-Potts field theories

We compute the crossover exponents of all quadratic and cubic deformations of critical field theories with permutation symmetry $S_q$ in $d=6-ε$ (Landau-Potts field theories) and $d=4-ε$ (hypertetrahedral models) up to three loops.We use our results to determine the $ε$-expansion of the fractal dimension of critical clusters in the most interesting cases, which include spanning trees and forests ($q\to0$), and bond percolations ($q\to1$). We also explicitly verify several expected degeneracies in the spectrum of relevant operators for natural values of $q$ upon analytic continuation, which are linked to logarithmic corrections of CFT correlators, and use the $ε$-expansion to determine the universal coefficients of such logarithms.

cond-mat.stat-mech↗

arXiv2020

On critical models with $N\leq 4$ scalars in $d=4-ε$

We adopt a combination of analytical and numerical methods to study the renormalization group flow of the most general field theory with quartic interaction in $d=4-ε$ with $N=3$ and $N=4$ scalars. For $N=3$, we find that it admits only three nondecomposable critical points: the Wilson-Fisher with $O(3)$ symmetry, the cubic with $H_3=(\mathbb{Z}_2)^3\rtimes S_3$ symmetry, and the biconical with $O(2)\times \mathbb{Z}_2$. For $N=4$, our analysis reveals the existence of new nontrivial solutions with discrete symmetries and with up to three distinct field anomalous dimensions.

hep-th↗

arXiv2020

Critical reflections on asymptotically safe gravity

Asymptotic safety is a theoretical proposal for the ultraviolet completion of quantum field theories, in particular for quantum gravity. Significant progress on this program has led to a first characterization of the Reuter fixed point. Further advancement in our understanding of the nature of quantum spacetime requires addressing a number of open questions and challenges. Here, we aim at providing a critical reflection on the state of the art in the asymptotic safety program, specifying and elaborating on open questions of both technical and conceptual nature. We also point out systematic pathways, in various stages of practical implementation, towards answering them. Finally, we also take the opportunity to clarify some common misunderstandings regarding the program.

gr-qc↗

arXiv2020

Symmetry and universality of multi-field interactions in $6-ε$ dimensions

We outline a general strategy developed for the analysis of critical models, which we apply to obtain a heuristic classification of all universality classes with up to three field-theoretical scalar order parameters in $d=6-ε$ dimensions. As expected by the paradigm of universality, each class is uniquely characterized by its symmetry group and by a set of its scaling properties, neither of which are built-in by the formalism but instead emerge nontrivially as outputs of our computations. For three fields, we find several solutions mostly with discrete symmetries. These are nontrivial conformal field theory candidates in less than six dimensions, one of which is a new perturbatively unitary critical model.

hep-th↗

arXiv2020

Wilsonian Renormalization Group In The Functional Nonperturbative Approach

We consider a functional relation between a given Wilsonian RG flow, which has to be related to a specific coarse-graining procedure, and an infinite family of (UV cutoff) scale dependent field redefinitions. Within this framework one can define a family of Wilsonian proper-time exact RG equations associated to an arbitrary regulator function. New applications of these RG flow schemes to the Ising Universality class in three dimensions in the derivative expansion are shortly illustrated.

hep-th↗

arXiv2019

The Odderon in QCD with running coupling

Starting from the leading Odderon solution of the three gluon system in perturbative QCD we introduce, as a first step towards the transition to the nonperturbative region, an infrared cutoff and use the running QCD coupling constant. In our numerical analysis we find that the fixed cut solution with intercept one persists, hinting at a physical Odderon with intercept one and a small t-slope.

hep-th↗

arXiv2019

The Fate of Dense Scalar Stars

Long-lived pseudo-solitonic objects, known as oscillons/oscillatons, which we collectively call real scalar stars, are ubiquitous in early Universe cosmology of scalar field theories. Typical examples are axions stars and moduli stars. Using numerical simulations in full general relativity to include the effects of gravity, we study the fate of real scalar stars and find that depending on the scalar potential they are either meta-stable or collapse to black holes. In particular we find that for KKLT potentials the configurations are meta-stable despite the asymmetry of the potential, consistently with the results from lattice simulations that do not include gravitational effects. For $α$-attractor potentials collapse to black holes is possible in a region of the parameter space where scalar stars would instead seem to be meta-stable or even disperse without including gravity. Each case gives rise to different cosmological implications which may affect the stochastic spectrum of gravitational waves.

gr-qc↗

arXiv2019

Leading order CFT analysis of multi-scalar theories in d>2

We investigate multi-field multicritical scalar theories using CFT constraints on two- and three-point functions combined with the Schwinger-Dyson equation. This is done in general and without assuming any symmetry for the models, which we just define to admit a Landau-Ginzburg description that includes the most general critical interactions built from monomials of the form $ϕ_{i_1} \cdots ϕ_{i_m}$. For all such models we analyze to the leading order of the $ε$-expansion the anomalous dimensions of the fields and those of the composite quadratic operators. For models with even $m$ we extend the analysis to an infinite tower of composite operators of arbitrary order. The results are supplemented by the computation of some families of structure constants. We also find the equations which constrain the nontrivial critical theories at leading order and show that they coincide with the ones obtained with functional perturbative RG methods. This is done for the case $m=3$ as well as for all the even models. We ultimately specialize to $S_q$ symmetric models, which are related to the $q$-state Potts universality class, and focus on three realizations appearing below the upper critical dimensions $6$, $4$ and $\frac{10}{3}$, which can thus be nontrivial CFTs in three dimensions.

hep-th↗