Renormalizable Theory Research Articles

Effective Kähler and auxiliary field potentials for chiral superfield models at three loops

I obtain the effective Kähler potential at three-loop order for a general renormalizable supersymmetric theory containing only chiral supermultiplets. The three-loop contribution is remarkably simple, consisting of only four terms involving three distinct renormalized master integrals. In the case of the Wess-Zumino model with a single chiral superfield, I also obtain the effective auxiliary field potential at three-loop order, extending previous results at one-loop order. The method used is inferential, relying on existing knowledge of the ordinary scalar effective potential. Published by the American Physical Society 2024

Renormalizable quantum theory of gravity

Abstract The renormalizable quantum theory of gravity is constructed based on Vector Theory of Gravity. The possibility of the existence of spin two gravitons within the framework of this theory is shown. A number of different quantum gravitational effects are considered. The parameters of the post-Newtonian approximation of the Vector Theory of Gravity have been also found.

General quartic β-function at three loops

We determine the three-loop MS¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ extrm{MS}} $$\\end{document} quartic β-function for the most general renormalisable four-dimensional theories. A general parametrisation of the β-function is compared to known β-functions for specific theories to fix all coefficients. Three-loop β-functions for the cubic coupling and scalar mass terms also follow from the result, which is made available in software packages.

Gauge-invariant quantum fields

Gauge-invariant quantum fields are constructed in an Abelian power-counting renormalizable gauge theory with both scalar, vector and fermionic matter content. This extends previous results already obtained for the gauge-invariant description of the Higgs mode via a propagating gauge-invariant field. The renormalization of the model is studied in the Algebraic Renormalization approach. The decomposition of Slavnov–Taylor identities into separately invariant sectors is analyzed. We also comment on some non-renormalizable extensions of the model whose 1-PI Green’s functions are the flows of certain differential equations of the homogeneous Euler type, exactly resumming the dependence on a certain set of dim. 6 and dim. 8 derivative operators. The latter are identified uniquely by the condition that they span the mass and kinetic terms in the gauge-invariant dynamical fields. The construction can be extended to non-Abelian gauge groups.

Algebraic structure of the renormalization group in the renormalizable QFT theories

In this paper, we consider the group formed by finite renormalizations as an infinite-dimensional Lie group. It is demonstrated that for the finite renormalization of the gauge coupling constant, its generators [Formula: see text] with [Formula: see text] satisfy the commutation relations of the Witt algebra and, therefore, form its subalgebra. The commutation relations are also written for the more general case when finite renormalizations are made for both the coupling constant and matter fields. We also construct the generator of the Abelian subgroup corresponding to the changes of the renormalization scale. The explicit expressions for the renormalization group generators are written in the case when they act on the [Formula: see text]-function and the anomalous dimension. It is explained how the finite changes of these functions under the finite renormalizations can be obtained with the help of the exponential map.

Q-balls in the presence of attractive force

Q-balls are non-topological solitons in field theories whose stability is typically guaranteed by the existence of a global conserved charge. A classic realization is the Friedberg-Lee-Sirlin (FLS) Q-ball in a two-scalar system where a real scalar χ triggers symmetry breaking and confines a complex scalar Φ with a global U(1) symmetry. A quartic interaction κχ2|Φ|2 with κ > 0 is usually considered to produce a nontrivial Q-ball configuration, and this repulsive force contributes to its stability. On the other hand, the attractive cubic interaction Λχ|Φ|2 is generally allowed in a renormalizable theory and could induce an instability. In this paper, we study the behavior of the Q-ball under the influence of this attractive force which has been overlooked. We find approximate Q-ball solutions in the limit of weak and moderate force couplings using the thin-wall and thick-wall approximations respectively. Our analytical results are consistent with numerical simulations and predict the parameter dependencies of the maximum charge. A crucial difference with the ordinary FLS Q-ball is the existence of the maximum charge beyond which the Q-ball solution is classically unstable. Such a limitation of the charge fundamentally affects Q-ball formation in the early Universe and could plausibly lead to the formation of primordial black holes.

Effectively flat potential in the Friedberg–Lee–Sirlin model

The Friedberg–Lee–Sirlin (FLS) model is a well-known renormalizable theory of scalar fields that provides for the existence of non-topological solitons. Since this model was proposed, numerous works have been dedicated to studying its classical configurations and its general suitability for various physical problems in cosmology, quantum chromodynamics, etc. In this paper, we study how Q-balls in effective field theory (EFT) reproduce non-topological solitons in the full FLS theory. We obtain an analytical description of the simplified model and compare the results with numerical calculations and perturbation theory. We also study the condensation of charged bosons on the domain wall. A full numerical solution allows us to check the EFT methods for this problem. The latter analysis is based on the application of EFT methods to significantly inhomogeneous configurations. We give an interpretation of the results in terms of the shifted boson mass and the vacuum rearrangement.

Pauli-type coupling of spinors and curved spacetime

Abstract In this study we prove that the Pauli interaction---which is associated with a length parameter---emerges when the minimal coupling recipe is applied to the non-degenerate Dirac Lagrangian.
The conventional Dirac Lagrangian is rendered non-degenerate if supplemented by a particular term quadratic in the derivatives of the spinors.
For dimensional reasons, this non-degenerate Dirac Lagrangian is associated with a length parameter $\ell$.
It yields---just as the conventional degenerate Dirac Lagrangian---the standard free Dirac equation in Minkowski space as the $\ell$ terms cancel when setting up the Euler-Lagrange equations.
However, if the Dirac spinor is minimally coupled to gauge fields, then the length parameter~$\ell$ becomes a physical coupling constant yielding novel interactions.
For the U($1$) symmetry the Pauli coupling of fermions to electromagnetic fields arises, modifying the fermion's magnetic moment.
We discuss the impact of these findings on electrodynamics, and estimate the upper bound of the length parameter~$\ell$ from the yet existing discrepancy between the (SM) theory and measurement of the anomalous magnetic moment of light leptons.
This, and also recent studies of the renormalization theory, suggest that the Pauli coupling of leptons to the electromagnetic field is a necessary ingredient in QED, supporting the notion of a fundamental nature of the non-degenerate Dirac Lagrangian.

In a second step we then investigate how analogous ``Pauli-type'' couplings of gravity and matter arise if fermions are embedded in curved spacetime.
The diffeomorphism and Lorentz invariance of that system leads to an anomalous spin-torsion interaction and a curvature-dependent mass correction.
We calculate the mass correction in the De~Sitter geometry of vacuum with the cosmological constant $\Lambda$.
Possible implications for the existence of effective non-zero rest masses of neutrinos are addressed.
Finally, an outlook on the impact of mass correction on the physics of ``Big Bang'' cosmology, black holes, and of neutron stars is provided.

Radiation and reaction at one loop

We study classical radiation fields at next-to-leading order using the methods of scattering amplitudes. The fields of interest to us are sourced when two massive, point-like objects scatter inelastically, and can be computed from one-loop amplitudes. The real and imaginary parts of the amplitudes play important but physically distinct roles in the radiation field. We argue that the imaginary part captures the effects of radiation reaction. This aspect of radiation reaction is directly linked to cuts of one-loop amplitudes which expose Compton trees. We also discuss the fascinating interplay between renormalisation, radiation reaction and classical field theory from this perspective.

3D-Ising-type magnetic interactions stabilized by the extremely large uniaxial magnetocrystalline anisotropy in layered ferromagnetic Cr2Te3

We investigate the magnetocrystalline anisotropy, critical behavior, and magnetocaloric effect in ferromagnetic-layered Cr2Te3. We have studied the critical behavior around the Curie temperature (TC) using various techniques, including the modified Arrott plot (MAP), the Kouvel-Fisher method (KF), and critical isothermal analysis (CI). The derived critical exponents β = 0.353(4) and γ = 1.213(5) fall in between the three-dimensional (3D) Ising and 3D Heisenberg type models, suggesting complex magnetic interactions by not falling into any single universality class. On the other hand, the renormalization group theory, employing the experimentally obtained critical exponents, suggests 3D-Ising-type magnetic interactions decaying with distance as J(r) = r−4.89. We also observe an extremely large uniaxial magnetocrystalline anisotropy energy (MAE) of Ku = 2065 kJ/m3, the highest ever found in any CrxTey based systems, originating from the noncollinear ferromagnetic ground state as predicted from the first-principles calculations. The self-consistent renormalization theory (SCR) suggests Cr2Te3 to be an out-of-plane itinerant ferromagnet. Further, a maximum entropy change of -ΔSMmax≈ 2.08 J/kg − K is estimated around TC for the fields applied parallel to the c-axis.

Hierarchical characterization of thermoelectric performance in copper-based chalcogenide CsCu3S2: Unveiling the role of anharmonic lattice dynamics

Fundamental understanding of anharmonic lattice dynamics and heat conductance physics in crystalline compounds is critical for the development of thermoelectric energy conversion devices. Herein, we thoroughly investigate the microscopic mechanisms of thermal transport in CsCu3S2 by coupling the self-consistent phonon (SCP) theory with the linearized Wigner transport equation (LWTE). We explicitly consider both phonon energy shifts and broadening arising from both cubic and quartic anharmonicities, as well as diagonal/non-diagonal terms of heat flux operators in thermal conductivity. Our findings show that the strong anharmonicity of CsCu3S2 primarily arises from the presence of p-d anti-bonding hybridization between Cu and S atoms, coupled with the random oscillations of Cs atoms. Notably, the competition between phonon hardening described by the loop diagram and softening induced by the bubble diagram significantly influences particle-like propagation, predominantly reflected in group velocity and energy-conservation rule. Additionally, the electrical transport properties are determined by employing the precise momentum relaxation-time approximation (MRTA). At high temperatures, the thermoelectric performance of p-type CsCu3S2 reaches its optimum theoretical value of 0.94 along the in-plane direction based on advanced phonon renormalization theory. In striking contrast, the harmonic approximation theory significantly overestimates the thermoelectric efficiency at the same temperatures, rendering it an impractical expectation. Conversely, the first-order renormalization approach leads to a serious underestimation of the thermoelectric properties due to the over-correction of phonon energy. Our study not only reveals the pivotal role of anharmonic lattice dynamics in accurately assessing thermoelectric properties but also underscores the potential thermoelectric applications for novel copper-based chalcogenides.

Elaboration and characterization of a natural bentonite-poly(ethylene glycol) composite: Development of an exact theoretical study in function of the polymer-density

The first aim of this work was a systematic experimental and theoretical study of the basal-spacing and characteristics of X-rays diffraction-peaks (positions, intensities, crystallites size...), versus the polymer-density, for a natural bentonite-poly(ethylene glycol) composite. The natural bentonite was extracted from a deposit located in Eastern Rif chain of Morocco (near Nador-city). The basal distance and diffraction-peaks characteristics were measured using X-Rays Diffraction (XRD) method, first, for raw bentonite, and second, for bentonite-poly(ethylene glycol) composites. In particular, measurements reveal the existence of a series of montmorillonite-phases (crystallites) of different sizes within the composites. Afterwards, we have developed a powerful theoretical approach based on Renormalization Theory, and obtain exact scaling relations for the physical quantities of interest. We have compared our theoretical predictions with our experimental data dealt with the considered natural bentonite-poly(ethylene glycol) composites, and found that theory and experiment are in good agreement. Also, as a complementary experimental study, we achieved a detailed analysis of pure PEG, natural bentonite and Bentonite-PEG composites using the so-called Fourier Transform Infrared Spectroscopy (FTIR) tool. A comparison between these complexes show that the polymer-density affects drastically the stretching and bending vibration modes.

Non-analyticity of the S-matrix with spontaneously broken Lorentz invariance

We study the S-matrix of Goldstones in the renormalizable theory of a U(1) complex scalar at finite charge, i.e. in a state that breaks Lorentz invariance. The theory is weakly coupled so that this S-matrix exists at all energies. Unlike the Lorentz invariant case, the resulting S-matrix is not analytic in the exchanged (complexified) four-momentum. The non-analyticities stem from the LSZ reduction formula, as a consequence of the energy-dependent mixing between the radial and Goldstone modes.

Jiezi: An open-source Python software for simulating quantum transport based on non-equilibrium Green's function formalism

We present a Python-based open-source library named Jiezi, which provides the means of simulating the electronic transport properties of nanoscaled devices on the atomistic level. The key feature of Jiezi lies in its core algorithm, i.e., self-consistent orchestration between the non-equilibrium Green's function (NEGF) method and a Poisson's equation solver. Beyond the construction of the tight-binding (TB) Hamiltonian with empirical parameters for conventional materials, the package offers a comprehensive framework for constructing the Wannier-based Hamiltonian matrix, enabling the investigation of novel materials and their heterostructures. To expedite the solution of NEGF systems, a methodology based on renormalization theory is proposed for reducing the dimension of the Hamiltonian matrix. Additionally, we adopt a non-linear Poisson equation solver with no analytical approximation in this software. The software facilitates seamless integration with external tools for geometry and mesh generation and post-processing. In this paper, we present the main capabilities and workflow by demonstrating with a simulation for the carbon nanotube field-effect transistor (CNTFET). Program summaryProgram Title: JieziCPC Library link to program files:https://doi.org/10.17632/nk79kbtww4.1Developer's repository link:https://github.com/Jiezi-negf/JieziLicensing provisions: GPLv3Programming language: PythonNature of problem: Simulates the quantum transport property of nano-scaled transistors based on the predefined device structure and the material composition.Solution method: Solves the coupled Schrödinger equation and Poisson equation by NEGF and finite element method.

High-Energy Behavior of Scattering Amplitudes in Theories with Purely Virtual Particles

We study a class of renormalizable quantum field theories with purely virtual particles that exhibits nonrenormalizable behavior in the high-energy limit of scattering cross sections, which grow as powers of the center-of-mass energy squared and seems to violate unitarity bounds. We point out that the problem should be viewed as a violation of perturbativity, instead of unitarity, and show that the resummation of self energies fixes the issue. As an explicit example, we consider a class of O(N) theories at the leading order in the large-N expansion and show that the different quantization prescription of purely virtual particles takes care of the nonrenormalizable behavior, making the resummed cross sections to decrease at high energies and the amplitudes to satisfy the unitarity bounds. We compare the results to the case of theories with ghosts, where the resummation cannot change the behavior of cross sections due to certain cancellations in the high-energy expansion of the self energies. These results are particularly relevant for quantum gravity.

Higher-order gravity, finite action, and a safe beginning for the universe

General relativity allows for inhomogeneous and anisotropic universes with finite action. By contrast, in quadratic gravity such solutions obtain infinite action and are thus eliminated. What remains are homogeneous and isotropic solutions undergoing accelerated expansion, thereby automatically inducing an early inflationary phase. In this manner, semi-classical consistency may explain some of the basic, coarse-grained features of the early universe. This includes suitable initial conditions for the second law of thermodynamics, in the spirit of the Weyl curvature hypothesis. We note that quadratic gravity is a renormalisable theory and may admit an asymptotically safe regime at high energies, rendering the theory trustworthy to high energies. We also comment on theories containing curvature terms up to infinite derivative order, and on the contrast with no-boundary initial conditions.

Quantum Gravity Effective Action Provides Entropy of the Universe

The effective action in the renormalizable quantum theory of gravity provides entropy because the total Hamiltonian vanishes. Since it is a renormalization group invariant that is constant in the process of cosmic evolution, we can show conservation of entropy, which is an ansatz in the standard cosmology. Here, we study renormalizable quantum gravity that exhibits conformal dominance at high energy beyond the Planck scale. The current entropy of the universe is derived by calculating the effective action under the scenario of quantum gravity inflation caused by its dynamics. We then argue that ghost modes must be unphysical but are necessary for the Hamiltonian to vanish and for entropy to exist in gravitational systems.

Two loop renormalization of scalar theories using a geometric approach

We derive a general formula for two-loop counterterms in Effective Field Theories (EFTs) using a geometric approach. This formula allows the two-loop results of our previous paper to be applied to a wide range of theories. The two-loop results hold for loop graphs in EFTs where the interaction vertices contain operators of arbitrarily high dimension, but at most two derivatives. We also extend our previous one-loop result to include operators with an arbitrary number of derivatives, as long as there is at most one derivative acting on each field. The final result for the two-loop counterterms is written in terms of geometric quantities such as the Riemann curvature tensor of the scalar manifold and its covariant derivatives. As applications of our results, we give the two-loop counterterms and renormalization group equations for the O(n) EFT to dimension six, the scalar sector of the Standard Model Effective Field Theory (SMEFT) to dimension six, and chiral perturbation theory to order p6.

Light scalars at the cosmological collider

We study the self-energies of weakly interacting scalar fields in de Sitter space with one field much lighter than the Hubble scale. We argue that self-energies drastically simplify in this light limit. We illustrate this in theories with two scalar fields, one heavy and one light, interacting with one another through either cubic or quartic interactions. To regulate infrared divergences, we compute these self-energies in Euclidean de Sitter space and then carefully analytically continue to Lorentzian signature. In particular, we do this for the most general renormalizable theory of two scalar fields with even interactions to leading order in the coupling and the mass of the light field. These self-energies are determined by de Sitter sunset diagrams, whose analytic structure and UV divergences we derive. Even at very weak couplings, the light field can substantially change how the heavy field propagates over long distances. The light field’s existence may then be inferred from how it modifies the heavy field’s oscillatory contribution to the primordial bispectrum in the squeezed limit, i.e. its cosmological collider signal.

Apparently superluminal superfluids

We consider the superfluid phase of a specific renormalizable relativistic quantum field theory. We prove that, within the regime of validity of perturbation theory and of the superfluid effective theory, there are consistent and regular vortex solutions where the superfluid’s velocity field as traditionally defined smoothly interpolates between zero and arbitrarily large superluminal values. We show that this solution is free of instabilities and of superluminal excitations. We show that, in contrast, a generic vortex solution for an ordinary fluid does develop an instability if the velocity field becomes superluminal. All this questions the characterization of a superfluid velocity field as the actual velocity of “something”.