Renormalization Procedure Research Articles

The Weyl BMS group and Einstein\u2019s equations

We propose an extension of the BMS group, which we refer to as Weyl BMS or BMSW for short, that includes super-translations, local Weyl rescalings and arbitrary diffeomorphisms of the 2d sphere metric. After generalizing the Barnich-Troessaert bracket, we show that the Noether charges of the BMSW group provide a centerless representation of the BMSW Lie algebra at every cross section of null infinity. This result is tantamount to proving that the flux-balance laws for the Noether charges imply the validity of the asymptotic Einstein’s equations at null infinity. The extension requires a holographic renormalization procedure, which we construct without any dependence on background fields. The renormalized phase space of null infinity reveals new pairs of conjugate variables. Finally, we show that BMSW group elements label the gravitational vacua.

Independent Channel Method for Nanoribbons with Dislocation and Fano Defects

In 2D materials, the dislocation is a common structural defect at finite temperatures as its appearance reduces the free energy by rising entropy, whereas many clusters of atoms or molecules, called as Fano defects, can be adsorbed on their extensive surface. Herein, the electronic transport in a long square nanoribbon with planar dislocation and Fano defects is studied within the tight‐binding formalism including nearest‐ and next‐nearest‐neighbor hopping integrals. To this purpose, a new convolution method is developed to transform the nanoribbon into a set of independent channels, where a real‐space renormalization procedure is applied. Despite the almost unaltered densities of states, the ballistic transport of periodic nanoribbons is mostly destroyed by the introduction of such structural defects, except for several energies in the case of Fano defects, and dissimilar conductance spectra are found in these two analyzed cases.

Renormalized holographic entanglement entropy in Lovelock gravity

We study the renormalization of Entanglement Entropy in holographic CFTs dual to Lovelock gravity. It is known that the holographic EE in Lovelock gravity is given by the Jacobson-Myers (JM) functional. As usual, due to the divergent Weyl factor in the Fefferman-Graham expansion of the boundary metric for Asymptotically AdS spaces, this entropy functional is infinite. By considering the Kounterterm renormalization procedure, which utilizes extrinsic boundary counterterms in order to renormalize the on-shell Lovelock gravity action for AAdS spacetimes, we propose a new renormalization prescription for the Jacobson-Myers functional. We then explicitly show the cancellation of divergences in the EE up to next-to-leading order in the holographic radial coordinate, for the case of spherical entangling surfaces. Using this new renormalization prescription, we directly find the C−function candidates for odd and even dimensional CFTs dual to Lovelock gravity. Our results illustrate the notable improvement that the Kounterterm method affords over other approaches, as it is non-perturbative and does not require that the Lovelock theory has limiting Einstein behavior.

Self-renormalization of quasi-light-front correlators on the lattice

In applying large-momentum effective theory, renormalization of the Euclidean correlators in lattice regularization is a challenge due to linear divergences in the self-energy of Wilson lines. Based on lattice QCD matrix elements of the quasi-PDF operator at lattice spacing a=0.03fm ∼ 0.12fm with clover and overlap valence quarks on staggered and domain-wall sea, we design a strategy to disentangle the divergent renormalization factors from finite physics matrix elements, which can be matched to a continuum scheme at short distance such as dimensional regularization and minimal subtraction. Our results indicate that the renormalization factors are universal in the hadron state matrix elements. Moreover, the physical matrix elements appear independent of the valence fermion formulations. These conclusions remain valid even with HYP smearing which reduces the statistical errors albeit reducing control of the renormalization procedure. Moreover, we find a large non-perturbative effect in the popular RI/MOM and ratio renormalization scheme, suggesting favor of the hybrid renormalization procedure proposed recently.

Dust-Acoustic Wave Dispersion in Thermal Dusty Plasmas at Weak and Moderate Couplings

The dispersion of dust-acoustic waves (DAWs) in weakly and moderately coupled thermal dusty plasmas is studied in the framework of the linear density-response formalism with the static local-field correction for interdust interactions. The plasma medium composition and the charge of dust particles are simultaneously determined within a recently developed chemical model (Physical Review E, vol. 101, 063203, 2020) based on minimizing the Helmholtz free energy of the system under investigation. Stemming from the generalized Poisson-Boltzmann equation, the renormalization procedure is consistently applied to derive an interdust screened potential that takes into account the finiteness of dust grains. Within the framework of the Ornstein-Zernike relationship in the hypernetted chain approximation, the static structure factor of the dust component is evaluated to manifest the appearance of local extrema on its wavenumber dependence, thereby indicating the short-range order formation in the arrangement of dust particles with respect to one another. It is shown that the DAW dispersion law is completely governed by the static structure factor and, therefore, exhibits a nonmonotonic dependence on the wavenumber as well. In the long-wavelength limit, the acoustic-like behavior of the DAW dispersion is strictly confirmed and the corresponding phase speed, reduced in units of the dust thermal velocity, is ultimately expressed via the static structure factor at zero wavenumber.

Fully coupled functional equations for the quark sector of QCD

We present a comprehensive study of the quark sector of $2+1$ flavour QCD, based on a self-consistent treatment of the coupled system of Schwinger-Dyson equations for the quark propagator and the full quark-gluon vertex. The individual form factors of the quark-gluon vertex are expressed in a special tensor basis obtained from a set of gauge-invariant operators. The sole external ingredient used as input to our equations is the Landau gauge gluon propagator with $2+1$ dynamical quark flavours, obtained from studies with Schwinger-Dyson equations, the functional renormalisation group approach, and large volume lattice simulations. The appropriate renormalisation procedure required in order to self-consistently accommodate external inputs stemming from other functional approaches or the lattice is discussed in detail, and the value of the gauge coupling is accurately determined at two vastly separated renormalisation group scales. Our analysis establishes a clear hierarchy among the vertex form factors. We identify only three dominant ones, in agreement with previous results. The components of the quark propagator obtained from our approach are in excellent agreement with the results from Schwinger-Dyson equations, the functional renormalisation group, and lattice QCD simulation, a simple benchmark observable being the chiral condensate in the chiral limit, which is computed as $(245\,\textrm{MeV})^3$. The present approach has a wide range of applications, including the self-consistent computation of bound-state properties and finite temperature and density physics, which are briefly discussed.

Inverse renormalization group based on image super-resolution using deep convolutional networks

The inverse renormalization group is studied based on the image super-resolution using the deep convolutional neural networks. We consider the improved correlation configuration instead of spin configuration for the spin models, such as the two-dimensional Ising and three-state Potts models. We propose a block-cluster transformation as an alternative to the block-spin transformation in dealing with the improved estimators. In the framework of the dual Monte Carlo algorithm, the block-cluster transformation is regarded as a transformation in the graph degrees of freedom, whereas the block-spin transformation is that in the spin degrees of freedom. We demonstrate that the renormalized improved correlation configuration successfully reproduces the original configuration at all the temperatures by the super-resolution scheme. Using the rule of enlargement, we repeatedly make inverse renormalization procedure to generate larger correlation configurations. To connect thermodynamics, an approximate temperature rescaling is discussed. The enlarged systems generated using the super-resolution satisfy the finite-size scaling.

Note on the pragmatic mode-sum regularization method: Translational-splitting in a cosmological background

The point-splitting renormalization method offers a prescription to calculate finite expectation values of quadratic operators constructed from quantum fields in a general curved spacetime. It has been recently shown by Levi and Ori that when the background metric possesses an isometry, like stationary or spherically symmetric black holes, the method can be upgraded into a pragmatic procedure of renormalization that produces efficient numerical calculations. In this note we show that when the background enjoys three-dimensional spatial symmetries, like homogeneous expanding universes, the above pragmatic regularization technique reduces to the well established adiabatic regularization method.

Charge algebra in Al(A)dSn spacetimes

The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in n dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the minimal falloffs for conformal compactification. In particular, the boundary structure is allowed to fluctuate and plays the role of source yielding some symplectic flux at the boundary. Using the holographic renormalization procedure, the divergences are removed from the symplectic structure, which leads to finite expressions. The charges associated with boundary diffeomorphisms are generically non-vanishing, non-integrable and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions due to the presence of Weyl anomalies in the dual theory. The charge algebra exhibits a field-dependent 2-cocycle in odd dimensions. When the general framework is restricted to three-dimensional asymptotically AdS spacetimes with Dirichlet boundary conditions, the 2-cocycle reduces to the Brown-Henneaux central extension. The analysis is also specified to leaky boundary conditions in asymptotically locally (A)dS spacetimes that lead to the Λ-BMS asymptotic symmetry group. In the flat limit, the latter contracts into the BMS group in n dimensions.

Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for long-ranged quantum spin chains with or without disorder

The simplest Tree-Tensor-States (TTS) respecting the Parity and the Time-Reversal symmetries are studied in order to describe the ground states of long-ranged quantum spin chains with or without disorder. Explicit formulas are given for the one-point and two-point reduced density matrices that allow to compute any one-spin and two-spin observable. For Hamiltonians containing only one-body and two-body contributions, the energy of the TTS can be then evaluated and minimized in order to obtain the optimal parameters of the TTS. This variational optimization of the TTS parameters is compared with the traditional block-spin renormalization procedure based on the diagonalization of some intra-block renormalized Hamiltonian.

Diagrammatic approaches to RNA structures with trinucleotide repeats

Trinucleotide repeat expansion disorders are associated with the overexpansion of (CNG) repeats on the genome. Messenger RNA transcripts of sequences with greater than 60–100 (CNG) tandem units have been implicated in trinucleotide repeat expansion disorder pathogenesis. In this work, we develop a diagrammatic theory to study the structural diversity of these (CNG)n RNA sequences. Representing structural elements on the chain’s conformation by a set of graphs and employing elementary diagrammatic methods, we have formulated a renormalization procedure to re-sum these graphs and arrive at a closed-form expression for the ensemble partition function. With a simple approximation for the renormalization and applied to extended (CNG)n sequences, this theory can comprehensively capture an infinite set of conformations with any number and any combination of duplexes, hairpins, multiway junctions, and quadruplexes. To quantify the diversity of different (CNG)n ensembles, the analytical equations derived from the diagrammatic theory were solved numerically to derive equilibrium estimates for the secondary structural contents of the chains. The results suggest that the structural ensembles of (CNG)n repeat sequence with n ∼60 are surprisingly diverse, and the distribution is sensitive to the ability of the N nucleotide to make noncanonical pairs and whether the (CNG)n sequence can sustain stable quadruplexes. The results show how perturbations in the form of biases on the stabilities of the various structural motifs, duplexes, junctions, helices, and quadruplexes could affect the secondary structures of the chains and how these structures may switch when they are perturbed.

Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order

We propose a novel representation of differential scattering cross-sections that locally realises the direct cancellation of infrared singularities exhibited by its so-called real-emission and virtual degrees of freedom. We take advantage of the Loop-Tree Duality representation of each individual forward-scattering diagram and we prove that the ensuing expression is locally free of infrared divergences, applies at any perturbative order and for any process without initial-state collinear singularities. Divergences for loop momenta with large magnitudes are regulated using local ultraviolet counterterms that reproduce the usual Lagrangian renormalisation procedure of quantum field theories. Our representation is especially suited for a numerical implementation and we demonstrate its practical potential by computing fully numerically and without any IR counterterm the next-to-leading order accurate differential cross-section for the process e+e− → doverline{d} . We also show first results beyond next-to-leading order by computing interference terms part of the N4LO-accurate inclusive cross-section of a 1 → 2 + X scalar scattering process.

Conservation and integrability in lower-dimensional gravity

We address the questions of conservation and integrability of the charges in two and three-dimensional gravity theories at infinity. The analysis is performed in a framework that allows us to treat simultaneously asymptotically locally AdS and asymptotically locally flat spacetimes. In two dimensions, we start from a general class of models that includes JT and CGHS dilaton gravity theories, while in three dimensions, we work in Einstein gravity. In both cases, we construct the phase space and renormalize the divergences arising in the symplectic structure through a holographic renormalization procedure. We show that the charge expressions are generically finite, not conserved but can be made integrable by a field-dependent redefinition of the asymptotic symmetry parameters.

A nonlinear Schrödinger equation with fractional noise

We study a stochastic Schrödinger equation with a quadratic nonlinearity and a space-time fractional perturbation, in space dimension d ≤ 3 d\leq 3 . When the Hurst index is large enough, we prove local well-posedness of the problem using classical arguments. However, for a small Hurst index, even the interpretation of the equation needs some care. In this case, a renormalization procedure must come into the picture, leading to a Wick-type interpretation of the model. Our fixed-point argument then involves some specific regularization properties of the Schrödinger group, which allows us to cope with the strong irregularity of the solution.

The quantum electrodynamics physical (QED-P) theory to complement quantum electrodynamics (QED)

The electronic and muonic hydrogen energy levels are calculated very accurately [M. L. Eides, H. Grotch, and V. Shelyuto, Phys. Rep. 342, 63 (2001)] in Quantum Electrodynamics (QED) by coupling the Dirac Equation four vector c(α, I) current covariantly with the external electromagnetic (EM) field four vector in QED’s Interactive Representation. While QED has been extraordinarily successful computationally, it presents no physical description of the electron, or other charged leptons. The QED-Physical (QED-P) theory presented in this paper is equivalent to QED in that it is based only on the four-current c(α, I) that is the reason that QED is so accurate computationally. However, QED-P describes the electron geometrically through the internal time/coordinate operators derived directly from c(α, I) with no assumptions. QED-P’s internal coordinate operators define an electron Center of Charge (CoC) point vibrating rapidly in space and time in its unique vacuum, creating the current that produces the electron’s magnetic moment and spin, and eliminating the need for “intrinsic” properties. QED-P also cuts off the photon propagator in a natural way so that the electron self-energy is finite and ad hoc renormalization procedures are not necessary. The c α-Non Exclusion Principle states that, if QED accepts c(α, I) as the electron current operator because of the very accurate hydrogen energy levels calculated, then one must also accept the QED-P electron internal spatial and time coordinate operators (ISaTCO) derived directly from c(α, I) without any other assumptions. QED-P shows the electron to be in both spin states simultaneously, and it is the external EM field that forces the electron’s spin state to be measured up or down. QED-P describes the bizarre, and very different, situation illustrated in Fig. 1 when the electron and muon are located “inside” the spatially extended proton with their CoCs orbiting the proton at the speed of light in S energy states of hydrogen, shedding some insight into the proton radius puzzle. The electron only appears to be a point particle with intrinsic properties when observed/measured from the far field. The Dirac‐Maxwell‐Wilson Equations are derived directly from the electron ISaTCO, and its EM fields “look” like they are from a point particle in far field scattering experiments in the same way the electric field from a sphere with evenly distributed charge “e” looks like a point charge with the same charge in the far field (Gauss Law). A physical basis for Quantum Entanglement is derived that can be measured experimentally.

Renormalized site density functional theory

Site density functional theory (SDFT) provides a rigorous framework for statistical mechanics analysis of inhomogeneous molecular liquids. The key defining feature of these systems is the presence of two very distinct interactions scales (intra- and inter-molecular), and as such proper description of both effects is critical to the accuracy of the calculations. Current SDFT applications utilize the same approximation scheme for both interaction motifs, which negatively impacts the results. Dual space methodology, used in this work, alleviates this issue by providing the flexibility of evaluating part of the interactions in traditional field representation. For molecular liquid this translates into retaining density representation for inter-molecular interactions but describing stiff intra-molecular remainder by more appropriate conventional field based methods. This opens the way to decouple analysis of the two interactions scales—the idea which is developed further in this work for the case of homogeneous reference approximation of inter-molecular interactions. We demonstrate that by defining new collective variables, the behaviour of the original molecular liquid system at the inter-molecular level can be transformed to resemble that of an effective simple fluid mixture. The latter is linked to intra-molecular scale through renormalized interaction parameters. We illustrate this renormalization procedure for several types of diatomic liquids, showing that this approach cures many of the shortcomings of existing SDFT methods.

Effect of non-thermal electrons on ion-acoustic dressed solitons in unmagnetised plasmas

Nonlinear propagation of an ion-acoustic dressed soliton is studied in unmagnetised plasma consisting of ion, positron and non-thermal electron. The exact soliton solution is derived using the reductive perturbation method (RPM) with the help of renormalisation procedure. This exact solution reduces to the dressed soliton solution when Mach number is expanded in terms of soliton velocity. The effects of non-thermal electrons, soliton velocity and Mach number on the characteristics (amplitude, width and product of amplitude and square of width) of the KdV soliton, core structure, dressed soliton and exact soliton are discussed in detail.

Renormalization group theory of the generalized multi-vertex sine-Gordon model

Abstract We investigate the renormalization group theory of the generalized multi-vertex sine-Gordon model by employing the dimensional regularization method and also the Wilson renormalization group method. The vertex interaction is given by $\cos(k_j\cdot \phi)$, where $k_j$ ($j=1,2,\ldots,M$) are momentum vectors and $\phi$ is an $N$-component scalar field. The beta functions are calculated for the sine-Gordon model with multiple cosine interactions. The second-order correction in the renormalization procedure is given by the two-point scattering amplitude for tachyon scattering. We show that new vertex interaction with the momentum vector $k_{\ell}$ is generated from two vertex interactions with vectors $k_i$ and $k_j$ when $k_i$ and $k_j$ meet the condition $k_{\ell}=k_i\pm k_j$, called the triangle condition. A further condition $k_i\cdot k_j=\pm 1/2$ is required within the dimensional regularization method. The renormalization group equations form a set of closed equations when $\{k_j\}$ form an equilateral triangle for $N=2$ or a regular tetrahedron for $N=3$. The Wilsonian renormalization group method gives qualitatively the same result for beta functions.

Inverse Power Law Scaling of Energy Dissipation Rate in Nonequilibrium Reaction Networks.

The energy dissipation rate in a nonequilibrium reaction system can be determined by the reaction rates in the underlying reaction network. By developing a coarse-graining process in state space and a corresponding renormalization procedure for reaction rates, we find that energy dissipation rate has an inverse power-law dependence on the number of microscopic states in a coarse-grained state. The dissipation scaling law requires self-similarity of the underlying network, and the scaling exponent depends on the network structure and the probability flux correlation. Existence of the inverse dissipation scaling law is shown in realistic biochemical systems such as biochemical oscillators and microtubule-kinesin active flow systems.

On thermodynamics of AdS black holes with scalar hair

It has been known that in the presence of a scalar hair there would be a distinct additional contribution to the first law of black hole thermodynamics. While it has been checked in many examples, a deeper understanding of this issue is necessary. The thermodynamics of AdS black holes in Einstein-scalar gravity is studied by using the standard holographic renormalization procedure and the variation of the Hamiltonian via the Wald formalism. It is found that the first law requires a modification by including an additional term that has a particular form ∼〈O〉δϕs, with ϕs and 〈O〉 a new pair of thermodynamic conjugate variables. ϕs is the leading source term of the asymptotic fall-off of the scalar field near the AdS boundary, and 〈O〉 is precisely the response of the dual scalar operator from the holographic point of view. Some hairy black holes are constructed explicitly to check the first law of thermodynamics as well as the thermodynamic relations.