Villars Regularization Research Articles

Pauli–Villars Regularization of Kaluza–Klein Casimir Energy with Lorentz Symmetry

Abstract The Pauli–Villars regularization is appropriate to discuss the UV sensitivity of low-energy observables because it mimics how the contributions of new particles at high energies cancel large quantum corrections from the light particles in the effective field theory. We discuss the UV sensitivity of the Casimir energy density and pressure in an extra-dimensional model in this regularization scheme, and clarify the condition on the regulator fields to preserve the Lorentz symmetry of the vacuum state. Some of the conditions are automatically satisfied in spontaneously broken supersymmetric models, but supersymmetry is not enough to ensure the Lorentz symmetry. We show that the necessary regulators can be introduced as bulk fields. We also evaluate the Casimir energy density with such regulators, and its deviation from the result obtained in the analytic regularization.

Pauli–Villars Regularization for Some Models with Singular Perturbations

Pauli–Villars Regularization for Some Models with Singular Perturbations

The finite volume effects on the critical endpoint of chiral phase transition in Nambu–Jona-Lasinio model with different regularization schemes

In this paper, we study the influence of different regularization schemes on the critical endpoint (CEP) of chiral phase transition within a cubic box with volume [Formula: see text]. A two-flavor Nambu–Jona-Lasinio model at finite temperature [Formula: see text] and chemical potential [Formula: see text] is adopted as the effective model of the strong interacting matter. Due to the finite volume of the box, the momentum integral in gap equation is replaced by discrete summation, and an anti-periodic boundary condition for quark field is applied. We employ the Schwinger’s proper time and the Pauli–Villars regularization (PVR) schemes, respectively. It is found that the first-order phase transition line displays an intriguing “staircase” behavior, and eventually disappears as [Formula: see text] increases. In particular, there is no existence of the CEP for both regularization schemes in infinite volume limit [Formula: see text]. However, for the finite volume, the locations of the CEPs with proper time and PVR are determined, respectively.

Trace anomaly and induced action for a metric-scalar background

The conformal anomaly and anomaly-induced effective action represent useful and economic ways to describe semiclassical contributions to the action of gravity. We discuss the anomaly in the case when the background is formed by metric and scalar fields and formulate the induced action in two standard covariant forms. The analysis of induced action at low energies reveals existing connection to the renormalization group and effective potential. The classification of anomalous terms is extended to the scalar background and ambiguities in the total derivative terms in the anomaly are considered using Pauli–Villars regularization.

Opus on conformal symmetry of the Nambu–Goto versus Polyakov strings

I investigate the Nambu–Goto and Polyakov strings, accounting for higher-derivative terms in the emergent action for the metric tensor which are classically negligible for smooth metrics but revive quantumly. Using the conformal field theory technique by KPZ-DDK, I compute in the one-loop approximation the conformal dimension and the central charge which differs in the two cases, telling the Nambu–Goto and Polyakov strings apart. I confirm the results by explicit quantum field theory computations of the propagator and the energy–momentum tensor at one loop, using the Pauli–Villars regularization.

Torsion-induced chiral magnetic current in equilibrium

We study equilibrium transport properties of massless Dirac fermions at finite temperature and chemical potential in spacetime accompanied by torsion, which in four dimensions couples with Dirac fermions as an axial gauge field. In particular, we compute the current density at the linear order in the torsion as well as in an external magnetic field with the Pauli–Villars regularization, finding that an equilibrium current akin to the chiral magnetic current is locally induced. Such torsion can be realized in condensed matter systems along a screw dislocation line, around which localized and extended current distributions are predicted so as to be relevant to Dirac and Weyl semimetals. Furthermore, we compute the current density at the linear order in the torsion as well as in a Weyl node separation, which turns out to vanish in spite of being allowed from the symmetry perspective. Contrasts of our findings with torsion-induced currents from previous work are also discussed.

Exploring Anomalies by Many‐Body Correlations

The quantum anomaly is written alternatively into a form violating conservation laws or as non‐gauge invariant currents seen explicitly on the example of chiral anomaly. By reinterpreting the many‐body averaging, the connection to Pauli–Villars regularization is established which gives the anomalous term a new interpretation as arising from quantum fluctuations by many‐body correlations at short distances. This is exemplified using an effective many‐body quantum potential which realizes quantum Slater sums by classical calculations. It is shown that these quantum potentials avoid the quantum anomaly but approach the same anomalous result by many‐body correlations. Consequently, quantum anomalies might be a shortcut way of single‐particle field theory to account for many‐body effects. This conjecture is also supported since the chiral anomaly can be derived by a completely conserving quantum kinetic theory. A measure for the quality of quantum potentials is suggested to describe these quantum fluctuations in the mean energy. The derived quantum potentials might be used to describe quantum simulations in classical terms.

Dependence of the crossover zone on the regularization method in the two-flavor Nambu–Jona-Lasinio model

AbstractIn this article, we study the two-flavor Nambu and Jona-Lasinio (NJL) phase diagrams on the T–μ plane through three regularization methods. In one of these, we introduce an infrared three-momentum cutoff in addition to the usual ultraviolet regularization to the quark loop integrals and compare the obtained phase diagrams with those obtained from the NJL model with proper time regularization and Pauli–Villars regularization. We have found that the crossover appears as a band with a well-defined width in the T–μ plane. To determine the extension of the crossover zone, we propose a novel criterion, comparing it to another criterion that is commonly reported in the literature; we then obtain the phase diagrams for each criterion. We study the behavior of the phase diagrams under all these schemes, focusing on the influence of the regularization procedure on the crossover zone and the presence or absence of critical end points.

Axial-anomaly in noncommutative QED and Pauli–Villars regularization

We calculate the [Formula: see text](1) axial-anomaly in two and four dimensions using a modified path integral method coupled to a Pauli–Villars regulator field in the noncommutative QED. Pauli–Villars regularization method provides us with unambiguous way to connect the modified path integral formalism with perturbative axial Ward identities at each step of calculations.

Light front Hamiltonian for boson form of QED (1 + 1) in Pauli–Villars regularization

Light front (LF) Hamiltonian for QED in [Formula: see text] dimensions is constructed using the boson form of this model with additional Pauli–Villars-type ultraviolet regularization. Perturbation theory, generated by this LF Hamiltonian, is proved to be equivalent to usual covariant chiral perturbation theory. The obtained LF Hamiltonian depends explicitly on chiral condensate parameters which enter in a form of some renormalization of coupling constants. The obtained results can be useful when one attempts to apply LF Hamiltonian approach for [Formula: see text]-dimensional models like QCD.

Gravitational Friedel oscillations in higher-derivative and infinite-derivative gravity?

When a positively charged impurity is placed inside a cold metal, the resulting charge density around that object exhibits characteristic ripples to negative values, known as Friedel oscillations. In this essay, we describe a somewhat analogous effect in (i) linearized higher-derivative gravity and (ii) linearized infinite-derivative “ghost-free” gravity: when a gravitational impurity (point particle) is placed in Minkowski vacuum, the local energy density [Formula: see text] (with [Formula: see text]) exhibits oscillations to negative values. The wavelength of these oscillations is roughly given by (i) the Pauli–Villars regularization scale and (ii) the scale of nonlocality. We hence dub this phenomena gravitational Friedel oscillations.

Renormalization for a Scalar Field in an External Scalar Potential

The Pauli–Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential are isolated into a three-parameter local, covariant functional of the background potential. These divergences can be naturally absorbed into coupling constants of the potential, regarded as a dynamical object in its own right; here, this is demonstrated in detail for two different models of the field-potential coupling. There is a residual dependence on the logarithm of the potential, reminiscent of the renormalization group in fully-interacting quantum field theories; these terms are finite, but numerically dependent on an arbitrary mass or length parameter, which is purely a matter of convention. This work is one step in a program to elucidate boundary divergences by replacing a sharp boundary by a steeply-rising smooth potential.

Anomaly cancellation in effective supergravity theories from the heterotic string: Two simple examples

We use Pauli–Villars regularization to evaluate the conformal and chiral anomalies in the effective field theories from Z3 and Z7 compactifications of the heterotic string without Wilson lines. We show that parameters for Pauli–Villars chiral multiplets can be chosen in such a way that the anomaly is universal in the sense that its coefficient depends only on a single holomorphic function of the three diagonal moduli. It is therefore possible to cancel the anomaly by a generalization of the four-dimensional Green–Schwarz mechanism. In particular we are able to reproduce the results of a string calculation of the four-dimensional chiral anomaly for these two models.

Anomalous Lorentz and CPT violation from a local Chern–Simons-like term in the effective gauge-field action

We consider four-dimensional chiral gauge theories defined over a spacetime manifold with topology R3×S1 and periodic boundary conditions over the compact dimension. The effective gauge-field action is calculated for Abelian U(1) gauge fields Aμ(x) which depend on all four spacetime coordinates (including the coordinate x4∈S1 of the compact dimension) and have vanishing components A4(x) (implying trivial holonomies in the 4-direction). Our calculation shows that the effective gauge-field action contains a local Chern–Simons-like term which violates Lorentz and CPT invariance. This result is established perturbatively with a generalized Pauli–Villars regularization and nonperturbatively with a lattice regularization based on Ginsparg–Wilson fermions.

The use of Pauli–Villars regularization in string theory

The proper-time regularization of bosonic string reproduces the results of canonical quantization in a special scaling limit where the length in target space has to be renormalized. We repeat the analysis for the Pauli–Villars regularization and demonstrate the universality of the results. In the mean-field approximation, we compute the susceptibility anomalous dimension and show it equals 1/2. We discuss the relation with the previously known results on lattice strings.

A study of diquark and meson condensation in the Nambu–Jona-Lasinio model and Fermi momentum

Using a three- and four-dimensional Pauli–Villars regularization scheme, we investigate quark–antiquark and diquark condensation in the framework of the Nambu–Jona-Lasinio model. Using the particle Fermi momentum as a cutoff parameter, we study the energy gap width and coherence length for the meson condensate 〈\(q\bar q\) 〉. We also study the energy gap width and critical coherence length (the distance over which there would be no diquark condensation) for the diquark 〈qq〉 and the dependence on the Fermi momentum. We obtain an estimate of the Fermi momentum value for meson and diquark condensates with an energy gap width of the order of 100 MeV.

Meson and diquark condensates in the NJL model and the Fermi momentum

Quark–anti quark and diquark condensation have been investigated in the framework of the NJL model. The Pauli–Villars regularization scheme have been used for the investigation of meson condensation in three dimension whereas the four dimensional case has been studied using the Schwinger–Dyson equation considering the Hartree approximation. Diquark condensation in three and four dimension have also been studied considering the Pauli–Villars regularization scheme. Using the Fermi momentum [Formula: see text] of the particle as cut-off parameter, the gap energy/coherence length for meson condensation [Formula: see text] have been investigated whereas for diquark [Formula: see text] the critical gap energy/critical coherence length (the distance over which there would be no diquark condensation) have been extracted. The variation of the coherence length/gap energy with [Formula: see text] have also been investigated. The results are compared with exciting data. Some interesting observations are made.

Pauli–Villars Regularization of Non-Abelian Gauge Theories

As an extension of earlier work on QED, we construct a BRST-invariant Lagrangian for SU(N) Yang-Mills theory with fundamental matter, regulated by the inclusion of massive Pauli-Villars (PV) gluons and PV quarks. The underlying gauge symmetry for massless PV gluons is generalized to accommodate the PV-index-changing currents that are required by the regularization. Auxiliary adjoint scalars are used, in a mechanism due to Stueckelberg, to attribute mass to the PV gluons and the PV quarks. The addition of Faddeev--Popov ghosts then establishes a residual BRST symmetry. Although there are drawbacks to the approach, in particular the computational load of a large number of PV fields and a nonlocal interaction of the ghost fields, this formulation could provide a foundation for renormalizable nonperturbative solutions of light-front QCD in an arbitrary covariant gauge.

Quantum supergravity, supergravity anomalies and string phenomenology

I discuss the role of quantum effects in the phenomenology of effective supergravity theories from compactification of the weakly coupled heterotic string. An accurate incorporation of these effects requires a regularization procedure that respects local supersymmetry and BRST invariance and that retains information associated with the cut-off scale, which has physical meaning in an effective theory. I briefly outline the Pauli–Villars regularization procedure, describe some applications, and comment on what remains to be done to fully define the effective quantum field theory.

On the possible dynamical realization of the Pauli–Villars regularization

The problem of free-particle scattering on virtual wormholes is considered. It is shown that, for all types of relativistic fields, this scattering leads to the appearance of additional very heavy particles, which play the role of auxiliary fields in the invariant scheme of Pauli–Villars regularization. A nonlinear correction that describes the back reaction of particles to the vacuum distribution of virtual wormholes is also obtained.