arXiv subjects

Carlo Pagani

Publications and source records attributed to Carlo Pagani.

At least 19 recordsLinked to original sources

arXiv2025

Explicit construction of the energy-momentum tensor in the large N limit

We construct the energy-momentum tensor of the O(N) linear sigma model explicitly in the large N limit using the exact renormalization group (ERG) formalism. The energy-momentum tensor is obtained as a cutoff dependent functional of N scalar field variables. Our guiding principles behind the construction are twofold: first the energy-momentum tensor must satisfy the Ward identity for translation and rotation invariance, and second the energy-momentum tensor must satisfy a variant of the exact renormalization group equation. In the limit that the momentum cutoff goes to zero, our energy-momentum tensor gives the one-particle irreducible (1PI) effective action with the insertion of a single energy-momentum tensor operator. We verify that the energy-momentum tensor constructed satisfies the expected trace formula, and that the trace vanishes at the Wilson-Fisher critical point.

hep-th↗

arXiv2025

A look at the operator product expansion in critical dynamics

We consider the critical relaxation of the Ising model, the so-called model A, and study its operator product expansion. Within perturbation theory, we focus on the operator product expansions of the two-point function and the response function. At the fixed point, we normalize the coefficients and the scaling variables so that the result displays universality. The role of the fluctuation-dissipation theorem is also discussed, and it is shown that it provides non-perturbative relations among the operator product expansion coefficients. Finally, the large N limit is considered.

cond-mat.stat-mech↗

arXiv2024

Background dependent cutoff for Wilson actions

We study the application of the background field method in the framework of the exact renormalization group (ERG). By considering the case of a scalar field theory, we provide a detailed discussion of the properties satisfied by a background dependent Wilson action. We show how the Ward identity associated with background field shifts for the Wilson action is related to that for the 1PI Wilson action, or effective average action. Moreover, we discuss the ERG equations in the dimensionless framework and emphasize the role of the Ward identity in this setting. We give two examples: the Gaussian fixed point for the real scalar theory and the large $N$ limit of the linear sigma model.

hep-th↗

arXiv2024

On the field independent additive constant in Wilson actions

We discuss the field independent additive constant in Wilson actions carefully within the exact renormalization group formalism. The additive constant does not affect the correlation functions of fields normalized by the partition function, and for that reason it is often ignored. But it is an essential part of the partition function, and in the limit where the UV cutoff goes to zero, the constant gives a renormalized vacuum energy density. We discuss two concrete examples: the Gaussian theory and the linear sigma model in the large $N$ limit.

hep-th↗

arXiv2022

Time evolution of density matrices as a theory of random surfaces

In the operatorial formulation of quantum statistics, the time evolution of density matrices is governed by von Neumann's equation. Within the phase space formulation of quantum mechanics it translates into Moyal's equation, and a formal solution of the latter is provided by Marinov's path integral. In this paper we uncover a hidden property of the Marinov path integral, demonstrating that it describes a theory of ruled random surfaces in phase space.

hep-th↗

arXiv2022

Operator product expansion coefficients from the nonperturbative functional renormalization group

Using the nonperturbative functional renormalization group (FRG) within the Blaizot-Méndez-Galain-Wschebor approximation, we compute the operator product expansion (OPE) coefficient $c_{112}$ associated with the operators $\mathcal{O}_1\simφ$ and $\mathcal{O}_2\simφ^2$ in the three-dimensional $\mathrm{O}(N)$ universality class and in the Ising universality class ($N=1$) in dimensions $2 \leq d \leq 4$. When available, exact results and estimates from the conformal bootstrap and Monte-Carlo simulations compare extremely well to our results, while FRG is able to provide values across the whole range of $d$ and $N$ considered.

hep-th↗

arXiv2021

Eulerian spatio-temporal correlations in passive scalar turbulence

We study the spatio-temporal two-point correlation function of passively advected scalar fields in the inertial-convective range in three dimensions by means of numerical simulations. We show that at small time delays $t$ the correlations decay as a Gaussian in the variable $tp$ where $p$ is the wavenumber. At large time delays, a crossover to an exponential decay in $tp^2$ is expected from a recent functional renormalization group (FRG) analysis. We study this regime for a scalar field advected by a Kraichnan's ``synthetic'' velocity field, and accurately confirm the FRG result, including the form of the prefactor in the exponential. By introducing finite time correlations in the synthetic velocity field, we uncover the crossover between the two regimes.

physics.flu-dyn↗

arXiv2021

Spatio-temporal correlation functions in scalar turbulence from functional renormalization group

We provide the leading behavior at large wavenumbers of the two-point correlation function of a scalar field passively advected by a turbulent flow. We first consider the Kraichnan model, in which the turbulent carrier flow is modeled by a stochastic vector field with a Gaussian distribution, and then a scalar advected by a homogeneous and isotropic turbulent flow described by the Navier-Stokes equation, under the assumption that the scalar is passive, i.e. that it does not affect the carrier flow. We show that at large wavenumbers, the two-point correlation function of the scalar in the Kraichnan model decays as an exponential in the time delay, in both the inertial and dissipation ranges. We establish the expression, both from a perturbative and from a nonperturbative calculation, of the prefactor, which is found to be always proportional to $k^2$. For a real scalar, the decay is Gaussian in $t$ at small time delays, and it crosses over to an exponential only at large $t$. The assumption of delta-correlation in time of the stochastic velocity field in the Kraichnan model hence significantly alters the statistical temporal behavior of the scalar at small times.

physics.flu-dyn↗

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↗

arXiv2019

Background Independent Quantum Field Theory and Gravitating Vacuum Fluctuations

The scale dependent effective average action for quantum gravity complies with the fundamental principle of Background Independence. Ultimately the background metric it formally depends on is selected self-consistently by means of a suitable generalization of Einstein's equation. Self-consistent backround spacetimes are scale dependent, and therefore "going on-shell" at the points along a given renormalization group (RG) trajectory requires understanding two types of scale dependencies: the (familiar) direct one carried by the off-shell action functional, and an indirect one related to the self-consistent background geometry. This paper is devoted to a careful delineation and analysis of certain general questions concerning the indirect scale dependence, as well as a detailed explicit investigation of the case where the self-consistent metrics are determined predominantly by the RG running of the cosmological constant. Mathematically, the object of interest is the spectral flow induced by the background Laplacian which, on-shell, acquires an explicit scale dependence. It encodes the information about the specific set of field modes which, at any given scale, are the degrees of freedom constituting the respective effective field theory. For a large class of RG trajectories we discover a seemingly paradoxical behavior: the theory looses rather than gains degrees of freedom at increasing energies. As an application, we investigate to what extent it is possible to reformulate the exact theory in terms of matter and gravity fluctuations on a rigid flat space. It turns out that, in vacuo, this "rigid picture" breaks down after a very short RG time. Furthermore, we reanalyze, and refute the claim that the huge energy densities one obtains in standard quantum field theory by summing up to zero-point energies imply a naturalness problem for the observed small value of the cosmological constant.

gr-qc↗

arXiv2019

Geometric operators in the asymptotic safety scenario for quantum gravity

We consider geometric operators, such as the geodesic length and the volume of hypersurfaces, in the context of the Asymptotic Safety scenario for quantum gravity. We discuss the role of these operators from the Asymptotic Safety perspective, and compute their anomalous dimensions within the Einstein-Hilbert truncation. We also discuss certain subtleties arising in the definition of such geometric operators. Our results hint to an effective dimensional reduction of the considered geometric operators.

gr-qc↗

arXiv2019

The International Linear Collider. A European Perspective

The International Linear Collider (ILC) being proposed in Japan is an electron-positron linear collider with an initial energy of 250 GeV. The ILC accelerator is based on the technology of superconducting radio-frequency cavities. This technology has reached a mature stage in the European XFEL project and is now widely used. The ILC will start by measuring the Higgs properties, providing high-precision and model-independent determinations of its parameters. The ILC at 250 GeV will also search for direct new physics in exotic Higgs decays and in pair-production of weakly interacting particles. The use of polarised electron and positron beams opens new capabilities and scenarios that add to the physics reach. The ILC can be upgraded to higher energy, enabling precision studies of the top quark and measurement of the top Yukawa coupling and the Higgs self-coupling. The international -- including European -- interest for the project is very strong. Europe has participated in the ILC project since its early conception and plays a major role in its present development covering most of its scientific and technological aspects: physics studies, accelerator and detectors. The potential for a wide participation of European groups and laboratories is thus high, including important opportunities for European industry. Following decades of technical development, R&D, and design optimisation, the project is ready for construction and the European particle physics community, technological centers and industry are prepared to participate in this challenging endeavour.

hep-ex↗

arXiv2019

The International Linear Collider. A Global Project

A large, world-wide community of physicists is working to realise an exceptional physics program of energy-frontier, electron-positron collisions with the International Linear Collider (ILC). This program will begin with a central focus on high-precision and model-independent measurements of the Higgs boson couplings. This method of searching for new physics beyond the Standard Model is orthogonal to and complements the LHC physics program. The ILC at 250 GeV will also search for direct new physics in exotic Higgs decays and in pair-production of weakly interacting particles. Polarised electron and positron beams add unique opportunities to the physics reach. The ILC can be upgraded to higher energy, enabling precision studies of the top quark and measurement of the top Yukawa coupling and the Higgs self-coupling. The key accelerator technology, superconducting radio-frequency cavities, has matured. Optimised collider and detector designs, and associated physics analyses, were presented in the ILC Technical Design Report, signed by 2400 scientists. There is a strong interest in Japan to host this international effort. A detailed review of the many aspects of the project is nearing a conclusion in Japan. Now the Japanese government is preparing for a decision on the next phase of international negotiations, that could lead to a project start within a few years. The potential timeline of the ILC project includes an initial phase of about 4 years to obtain international agreements, complete engineering design and prepare construction, and form the requisite international collaboration, followed by a construction phase of 9 years.

hep-ex↗

arXiv2018

Stationary, isotropic and homogeneous two-dimensional turbulence: a first non-perturbative renormalization group approach

We study the statistical properties of stationary, isotropic and homogeneous turbulence in two-dimensional (2D) flows, focusing on the direct cascade, that is on wave-numbers large compared to the integral scale, where both energy and enstrophy are provided to the fluid. Our starting point is the 2D Navier-Stokes equation in the presence of a stochastic forcing, or more precisely the associated field theory. We unveil two extended symmetries of the Navier-Stokes action which were not identified yet, one related to time-dependent (or time-gauged) shifts of the response fields and existing in both 2D and 3D, and the other to time-gauged rotations and specific to 2D flows. We derive the corresponding Ward identities, and exploit them within the non-perturbative renormalization group formalism, and the large wave-number expansion scheme developed in [Phys. Fluids {\bf 30}, 055102 (2018)]. We consider the flow equation for a generalized $n$-point correlation function, and calculate its leading order term in the large wave-number expansion. At this order, the resulting flow equation can be closed exactly. We solve the fixed point equation for the 2-point function, which yields its explicit time dependence, for both small and large time delays in the stationary turbulent state. On the other hand, at equal times, the leading order term vanishes, so we compute the next-to-leading order term. We find that the flow equations for simultaneous $n$-point correlation functions are not fully constrained by the set of extended symmetries, and discuss the consequences.

cond-mat.stat-mech↗

arXiv2018

Finite Entanglement Entropy in Asymptotically Safe Quantum Gravity

Entanglement entropies calculated in the framework of quantum field theory on classical, flat or curved, spacetimes are known to show an intriguing area law in four dimensions, but they are also notorious for their quadratic ultraviolet divergences. In this paper we demonstrate that the analogous entanglement entropies when computed within the Asymptotic Safety approach to background independent quantum gravity are perfectly free from such divergences. We argue that the divergences are an artifact due to the over-idealization of a rigid, classical spacetime geometry which is insensitive to the quantum dynamics.

gr-qc↗

arXiv2018

Functional Renormalization Group approach to the Kraichnan model

We study the anomalous scaling of the structure functions of a scalar field advected by a random Gaussian velocity field, the Kraichnan model, by means of Functional Renormalization Group techniques. We analyze the symmetries of the model and derive the leading correction to the structure functions considering the renormalization of composite operators and applying the operator product expansion.

cond-mat.stat-mech↗

arXiv2017

Note on the super-extended Moyal formalism and its BBGKY hierarchy

We consider the path integral associated to the Moyal formalism for quantum mechanics extended to contain higher differential forms by means of Grassmann odd fields. After revisiting some properties of the functional integral associated to the (super-extended) Moyal formalism, we give a convenient functional derivation of the BBGKY hierarchy in this framework. In this case the distribution functions depend also on the Grassmann odd fields.

cond-mat.stat-mech↗

arXiv2017

Composite Operators in Asymptotic Safety

We study the role of composite operators in the Asymptotic Safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this set-up allows to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings, including Quantum Einstein Gravity, the conformally reduced Einstein-Hilbert truncation, and two dimensional quantum gravity. Finally, we briefly argue that our construction paves the way to approach observables in the Asymptotic Safety program.

gr-qc↗