arXiv subjects

Omar Zanusso

Publications and source records attributed to Omar Zanusso.

At least 37 records · Page 2Linked to original sources

arXiv2021

Gravity in $d=2+ε$ dimensions and realizations of the diffeomorphisms group

We discuss two distinct realizations of the diffeomorphism group for metric gravity, which give rise to theories that are classically equivalent, but quantum mechanically distinct. We renormalize them in $d=2+ε$ dimensions, developing a new procedure for dimensional continuation of metric theories and highlighting connections with the constructions that previously appeared in the literature. Our hope is to frame candidates ultraviolet completions of quantum gravity in $d>2$ and give some perturbative mean to assess its existence in $d=4$, but also to speculate on some potential obstructions in the continuation of such candidates to finite values of $ε$. Our results suggest the presence of a conformal window in $d$ which seems to extend to values higher than four.

hep-th↗

arXiv2021

Multicritical hypercubic models

We study renormalization group multicritical fixed points in the $ε$-expansion of scalar field theories characterized by the symmetry of the (hyper)cubic point group $H_N$. After reviewing the algebra of $H_N$-invariant polynomials and arguing that there can be an entire family of multicritical (hyper)cubic solutions with $ϕ^{2n}$ interactions in $d=\frac{2n}{n-1}-ε$ dimensions, we use the general multicomponent beta functionals formalism to study the special cases $d = 3-ε$ and $d =\frac{8}{3}-ε$, deriving explicitly the beta functions describing the flow of three- and four-critical (hyper)cubic models. We perform a study of their fixed points, critical exponents and quadratic deformations for various values of $N$, including the limit $N=0$, that was reported in another paper in relation to the randomly diluted single-spin models, and an analysis of the large $N$ limit, which turns out to be particularly interesting since it depends on the specific multicriticality. We see that, in general, the continuation in $N$ of the random solutions is different from the continuation coming from large-$N$, and only the latter interpolates with the physically interesting cases of low-$N$ such as $N=3$. Finally, we also include an analysis of a theory with quintic interactions in $d =\frac{10}{3}-ε$ and, for completeness, the NNLO computations in $d=4-ε$.

hep-th↗

arXiv2020

RG and logarithmic CFT multicritical properties of randomly diluted Ising models

We discuss how a spin system, which is subject to quenched disorder, might exhibit multicritical behaviors at criticality if the distribution of the impurities is arbitrary. In order to provide realistic candidates for such multicritical behaviors, we discuss several generalizations of the standard randomly diluted Ising's universality class adopting the $ε$-expansion close to several upper critical dimensions. In the presentation, we spend a special effort in bridging between CFT and RG results and discuss in detail the computation of quantities, which are of prominent interest in the case of logarithmic CFT.

hep-th↗

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

Fractal geometry of higher derivative gravity

We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal dimensions of such hypersurfaces embedded in a quantum spacetime at very small distances.

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↗

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↗

arXiv2019

Renormalization of multicritical scalar models in curved space

We consider the leading order perturbative renormalization of the multicritical $ϕ^{2n}$ models and some generalizations in curved space. We pay particular attention to the nonminimal interaction with the scalar curvature $\frac{1}{2}ξϕ^2 R$ and discuss the emergence of the conformal value of the coupling $ξ$ as the renormalization group fixed point of its beta function at and below the upper critical dimension as a function of $n$. We also examine our results in relation with Kawai and Ninomiya's formulation of two dimensional gravity.

hep-th↗

arXiv2019

Vacuum effective actions and mass-dependent renormalization in curved space

We review past and present results on the non-local form-factors of the effective action of semiclassical gravity in two and four dimensions computed by means of a covariant expansion of the heat kernel up to the second order in the curvatures. We discuss the importance of these form-factors in the construction of mass-dependent beta functions for the Newton's constant and the other gravitational couplings.

hep-th↗

arXiv2019

Form factors and decoupling of matter fields in four-dimensional gravity

We extend previous calculations of the non-local form factors of semiclassical gravity in $4D$ to include the Einstein-Hilbert term. The quantized fields are massive scalar, fermion and vector fields. The non-local form factor in this case can be seen as the sum of a power series of total derivatives, but it enables us to derive the beta function of Newton's constant and formally evaluate the decoupling law in the new sector, which turns out to be the standard quadratic one.

hep-th↗

arXiv2018

Gravitational form factors and decoupling in 2D

We calculate and analyse non-local gravitational form factors induced by quantum matter fields in curved two-dimensional space. The calculations are performed for scalars, spinors and massive vectors by means of the covariant heat kernel method up to the second order in the curvature and confirmed using Feynman diagrams. The analysis of the ultraviolet (UV) limit reveals a generalized "running" form of the Polyakov action for a nonminimal scalar field and the usual Polyakov action in the conformally invariant cases. In the infrared (IR) we establish the gravitational decoupling theorem, which can be seen directly from the form factors or from the physical beta function for fields of any spin.

hep-th↗

arXiv2018

Functional perturbative RG and CFT data in the $ε$-expansion

We show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for a given universality class. The task is greatly simplified by a straightforward generalization of perturbation theory to a functional perturbative RG approach. We illustrate our procedure in the $ε$-expansion by obtaining the next-to-leading corrections for the spectrum and the leading corrections for the OPE coefficients of Ising and Lee-Yang universality classes and then give several results for the whole family of renormalizable multicritical models $ϕ^{2n}$. Whenever comparison is possible our RG results explicitly match the ones recently derived in CFT frameworks.

hep-th↗

arXiv2018

A functional perspective on emergent supersymmetry

We investigate the emergence of ${\cal N}=1$ supersymmetry in the long-range behavior of three-dimensional parity-symmetric Yukawa systems. We discuss a renormalization approach that manifestly preserves supersymmetry whenever such symmetry is realized, and use it to prove that supersymmetry-breaking operators are irrelevant, thus proving that such operators are suppressed in the infrared. All our findings are illustrated with the aid of the $ε$-expansion and a functional variant of perturbation theory, but we provide numerical estimates of critical exponents that are based on the non-perturbative functional renormalization group.

hep-th↗

arXiv2017

Renormalization group flows and fixed points for a scalar field in curved space with nonminimal $F(ϕ)R$ coupling

Using covariant methods, we construct and explore the Wetterich equation for a non-minimal coupling $F(ϕ)R$ of a quantized scalar field to the Ricci scalar of a prescribed curved space. This includes the often considered non-minimal coupling $ξϕ^2 R$ as a special case. We consider the truncations without and with scale- and field-dependent wave function renormalization in dimensions between four and two. Thereby the main emphasis is on analytic and numerical solutions of the fixed point equations and the behavior in the vicinity of the corresponding fixed points. We determine the non-minimal coupling in the symmetric and spontaneously broken phases with vanishing and non-vanishing average fields, respectively. Using functional perturbative renormalization group methods, we discuss the leading universal contributions to the RG flow below the upper critical dimension $d=4$.

hep-th↗

arXiv2017

New universality class in three dimensions: The critical Blume-Capel model

We study the Blume-Capel universality class in $d=\frac{10}{3}-ε$ dimensions. The RG flow is extracted by looking at poles in fractional dimension of three loop diagrams using $\overline{\rm MS}$. The theory is the only nontrivial universality class which admits an expansion to three dimensions with $ε=\frac{1}{3}<1$. We compute the relevant scaling exponents and estimate some of the OPE coefficients to the leading order. Our findings agree with and complement CFT results. Finally we discuss a family of nonunitary multicritical models which includes the Lee-Yang and Blume-Capel classes as special cases.

hep-th↗

arXiv2017

Lee-Yang model from the functional renormalization group

We investigate the critical properties of the Lee-Yang model in less than six spacetime dimensions using truncations of the functional renormalization group flow. We give estimates for the critical exponents, study the dependence on the regularization scheme, and show the convergence of our results for increasing size of the truncations in four and five dimensions. While with our truncations it is numerically challenging to approach the three-dimensional case, we provide a simple approximation which allows us to qualitatively study the Lee-Yang model in two and three dimensions, and use it to argue the existence of further nonunitary multicritical theories including one which is relevant for the universality class of the Blume-Capel model.

hep-th↗