Axial-vector Fields Research Articles

General holographic chiral theory near a boundary

Because of the Weyl anomaly, the background axial vector field induces novel chiral currents near a boundary. Recently, a non-minimal holographic chiral model has been proposed to produce the expected chiral current. The critical point is adding a boundary mass term Aˆ2 of the axial vector field. This paper investigates the holographic chiral model with general boundary action in AdS/BCFT. We find the nonlinear gauge-violating boundary interactions V1(Aˆ2) generally lead to ghost instability and the singularity problem. On the other hand, the mass term Aˆ2 and gauge-invariant interactions V2(Fˆ2) are free of these issues. For the squared boundary action with mass and kinetic terms, we analyze the holographic chiral current near a boundary. We work out more subleading terms and verify they agree with the field-theoretical results. We find the boundary kinetic term affects only the finite term of chiral currents. Finally, we briefly comment on the applications of our model in cone double holography.

Non-Abelian Carroll–Field–Jackiw term in a Rarita-Schwinger model

In this paper, we demonstrate the possibility of generating a non-Abelian Carroll–Field–Jackiw (CFJ) term in the theory of a non-Abelian gauge field coupled to a spin-3/2 field in the presence of the constant axial vector field. Applying two regularization schemes, we prove that this term is finite and ambiguous, particularly vanishing within the 't Hooft-Veltman scheme.

Holographic anomalous chiral current near a boundary

Due to the Weyl anomaly, an axial vector field produces novel anomalous chiral currents in spacetime with boundaries. Remarkably, the chiral current is not invariant under the gauge transformation of axial vector fields. As a result, more potential terms appear, and the chiral current becomes larger than the electric current near the boundary. This paper investigates the anomalous chiral current in AdS/BCFT. We find that the minimal holographic model of the axial vector field cannot produce the expected chiral current. To resolve this problem, we propose adding a suitable boundary action. Furthermore, we notice a similar situation for holographic condensation. Finally, we obtain the shape dependence of holographic chiral current and verify that it agrees with the field-theoretical result.

Induced Chern-Simons term by dimensional reduction

We derive an induced Abelian Chern-Simons (CS) term in 2+1 dimensions, by dimensional reduction from the finite-temperature theory of a Dirac field with both vector and axial-vector couplings to two Abelian gauge fields, in 3+1 dimensions. In our construction, the CS term emerges for the lowest Matsubara mode of the vector Abelian field, by integrating the fermionic field, under the assumption that the axial vector field is in a "vacuum" configuration. This configuration is characterized by a single number, which in turn determines the coefficient of the induced CS term for the Abelian vector field.

Heat kernel, spectral functions and anomalies in Weyl semimetals

Being motivated by applications to the physics of Weyl semimetals we study spectral geometry of Dirac operator with an abelian gauge field and an axial vector field. We impose chiral bag boundary conditions with variable chiral phase θ on the fermions. We establish main properties of the spectral functions which ensure applicability of the ζ function regularization and of the usual heat kernel formulae for chiral and parity anomalies. We develop computational methods, including a perturbation expansion for the heat kernel. We show that the terms in both anomalies which include electromagnetic potential are independent of θ.

A_{1} meson-nucleon coupling constant at finite temperature from the soft-wall AdS/QCD model

We study the temperature dependence of the a_1 meson-nucleon coupling constant in the framework of the soft-wall AdS/QCD model with thermal dilaton field. Profile functions for the axial-vector and fermion fields in the AdS-Schwarzschild metric are presented. It is constructed an interaction Lagrangian for the fermion-axial-vector-thermal dilaton fields system in the bulk of space-time. From this Lagrangian integral representation for the g_{a_1NN} coupling constant is derived. The temperature dependence of this coupling constant is numerically analyzed.

Quantum kinetic equation for fluids of spin-1/2 fermions

Fluid of spin-1/2 fermions is represented by a complex scalar field and a four-vector field coupled both to the scalar and the Dirac fields. We present the underlying action and show that the resulting equations of motion are identical to the (hydrodynamic) Euler equations in the presence of Coriolis force. As a consequence of the gauge invariances of this action we established the quantum kinetic equation which takes account of noninertial properties of the fluid in the presence of electromagnetic fields. The equations of the field components of Wigner function in Clifford algebra basis are employed to construct new semiclassical covariant kinetic equations of the vector and axial-vector field components for massless as well as massive fermions. Nonrelativistic limit of the chiral kinetic equation is studied and shown that it generates a novel three-dimensional transport theory which does not depend on spatial variables explicitly and possesses a Coriolis force term. We demonstrated that the three-dimensional chiral transport equations are consistent with the chiral anomaly. For massive fermions the three-dimensional kinetic transport theory generated by the new covariant kinetic equations is established in small mass limit. It possesses the Coriolis force and the massless limit can be obtained directly.

A new approach to anomalous axial vector field theory – II

This work is continuation of a stochastic quantization program reported earlier. In this paper, we propose a consistent scheme of doing computations directly in four dimensions using conventional quantum field theory methods.

A new approach to anomalous axial vector field theory

In an earlier paper, it has been shown that the ultra violet divergence structure of anomalous [Formula: see text] axial vector gauge model in the stochastic quantization scheme is different from that in the conventional quantum field theory. Also, it has been shown that the model is expected to be renormalizable. Based on the operator formalism of the stochastic quantization, a new approach to anomalous [Formula: see text] axial vector gauge model is proposed. The operator formalism provides a convenient framework for analysis of ultra violet divergences, but the computations in a realistic model become complicated. In this paper a new approach to do computations in the model is formulated directly in four dimensions. The suggestions put forward here will lead to simplification in the study of applications of the axial vector gauge theory, as well as those of other similar models.

Topological piezoelectric effect and parity anomaly in nodal line semimetals

Lattice deformations act on the low-energy excitations of Dirac materials as effective axial vector fields. This allows to directly detect quantum anomalies of Dirac materials via the response to axial gauge fields. We investigate the parity anomaly in Dirac nodal line semimetals induced by lattice vibrations, and establish a topological piezoelectric effect; i.e., periodic lattice deformations generate topological Hall currents that are transverse to the deformation field. The currents induced by this piezoelectric effect are dissipationless and their magnitude is completely determined by the length of the nodal ring, leading to a semi-quantized transport coefficient. Our theoretical proposal can be experimentally realized in various nodal line semimetals, such as CaAgP and Ca$_{_3}$P${_2}$.

Axial anomaly generation by domain wall motion in Weyl semimetals

A space-time dependent node separation in Weyl semimetals acts as an axial vector field. Coupled with domain wall motion in magnetic Weyl semimetals, this induces axial electric and magnetic fields localized at the domain wall. We show how these fields can activate the axial (chiral) anomaly and provide a direct experimental signature of it. Specifically, a domain wall provides a spatially dependent Weyl node separation and an axial magnetic field $\textbf{B}_5$, and domain wall movement, driven by an external magnetic field, gives the Weyl node separation a time dependence, inducing an axial electric field $\textbf{E}_5$. At magnetic fields beyond the Walker breakdown, $\textbf{E}_5\cdot\textbf{B}_5$ becomes nonzero and activates the axial anomaly that induces a finite axial charge density -- imbalance in the number of left- and right-handed fermions -- moving with the domain wall. This axial density, in turn, produces, via the chiral magnetic effect, an oscillating current flowing along the domain wall plane, resulting in a characteristic radiation of electromagnetic waves emanating from the domain wall. A detection of this radiation would constitute a direct measurement of the axial anomaly induced by axial electromagnetic fields.

Maxwell Equations Derived from Coulomb’ Law vs. Maxwell-type Gravity Derived from Newton’s Law

A Universal Mathematical Field Theory (UMFT) is established and states that the combination of the operations of both gradient and divergence of vector fields, such as electric field and velocity field, create the curl of an axial vector field, such as magnetic field. Utilizing UMFT, Extended-Maxwell equations and the equation of Lorentz force are derived from the combination of Coulomb’s law and velocity of source mathematically, and new effects are predicted. For a source moving with non-spatially-varying velocity Extended-Maxwell equations reduce to Maxwell equations. This derivation mathematically explains how a moving electric charge creates magnetic field, and shows that there is no magnetic monopole charge. The duality between the Newton’s law and the Coulomb’s law leads us to derive Maxwell-type gravitational equations and Lorentz-type gravitational force by combining UMFT, the Newton’s law and velocity of gravitational source, denoted as Gravito-electromagnetic, which is dual of Electromagnetics. The benefits of the duality are that the effects and phenomena of Electromagnetics may be directly converted to that of gravity. The Gravito-Electromagnetics are employed to study the accelerating expansion of the universe, rotation curve, virial theorem, and gravitation radiation.

Galactic center constraints on self-interacting sterile neutrinos from fermionic dark matter (“ino”) models

The neutrino minimal standard model ($\nu$MSM) has been tightly constrained in the recent years, either from dark matter (DM) production or from X-ray and small-scale observations. However, current bounds on sterile neutrino DM can be significantly modified when considering a $\nu$MSM extension, in which the DM candidates interact via a massive (axial) vector field. In particular, standard production mechanisms in the early Universe can be affected through the decay of such a massive mediator. We perform an indirect detection analysis to study how the $\nu$MSM parameter-space constraints are affected by said interactions. We compute the X-ray fluxes considering a DM profile that self-consistently accounts for the particle physics model by using an updated version of the Ruffini-Arg\"uelles-Rueda (RAR) fermionic ("ino") model, instead of phenomenological profiles such as the Navarro-Frenk-White (NFW) distribution. We show that the RAR profile accounting for interacting DM, is compatible with measurements of the Galaxy rotation curve and constraints on the DM self-interacting cross section from the Bullet cluster. A new analysis of the X-ray NuSTAR data in the central parsec of the Milky Way, is here performed to derive constraints on the self-interacting sterile neutrino parameter-space. Such constraints are stronger than those obtained with commonly used DM profiles, due to the dense DM core characteristic of the RAR profiles.

The class of evolutionary ferrodynamic equations

The class of evolutionary equations for axial vector fields on is described. All operators of the class are invariant with respect to space translations in , relative to time translations, and they are transformed by covariant way relative to rotations of . The class of second‐order differential operators is studied such that the corresponding evolution equations have the divergent type and each of them preserves the solenoidal property and the unimodality of the field. The explicit form of such operators is found.

Minimal model of torsion mediated dark matter

We present a minimal model of fermionic dark matter (DM), where a singlet Dirac fermion can interact with the Standard Model (SM) particles via the torsion field of gravitational origin. In general, torsion can be realized as an antisymmetric part of the affine connection associated with the spacetime diffeomorphism symmetry and thus can be thought of as a massive axial vector field. Because of its gravitational origin, the torsion field couples to all the fermion fields including the DM with equal strength, which makes the model quite predictive. The DM is naturally stable without any imposition of ad-hoc symmetry {\it e.g.,} $\mathcal{Z}_2$. Apart from producing the correct thermal abundance, singlet fermion can easily evade the stringent bounds on the spin-independent DM-nucleon direct detection cross-section due to its axial nature. However, in the allowed parameter space, strong bounds can be placed on the torsion mass and its couplings to fermions from the recent LHC searches. Assuming a non universal torsion-DM and torsion-SM coupling, smaller values of torsion masses may become allowed. In both cases we also study the reach of spin-dependent direct detection searches of the DM.

A massive field-theoretic model for Hodge theory

Within the framework of Becchi–Rouet–Stora–Tyutin (BRST) formalism, we show that the four (3+1)-dimensional (4D) massive Abelian 2-form gauge theory (without any interaction with matter fields) is a model for the Hodge theory because its discrete and continuous symmetry transformations (and their corresponding Noether conserved charges) provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level. For this purpose, we incorporate the pseudo-scalar and axial-vector fields which appear in the theory with negative kinetic terms (but with proper definition of mass). The negative kinetic terms, for the above fields, are essential so that our theory could respect the discrete symmetry transformations which provide the physical realizations of the Hodge duality operation in the domain of differential geometry. Thus, our present endeavour, not only provides the physical realizations of all the mathematical ingredients connected with the de Rham cohomological operators of differential geometry, it also sheds light on the existence and emergence of fields with negative kinetic terms. We discuss the implications and relevance of the latter fields in the context of current models of dark matter and dark energy as well as the bouncing models of Universe.

Effects of K–K1 Transitions on Kaon-Field Renormalization in the NJL Model Framework

An additional kaon-field renormalization dictated by transitions between pseudoscalar and axial-vector fields is derived in the Nambu–Jona-Lasinio model framework. Possible mixings between the $${{K}_{{1A}}}$$ and $${{K}_{{1B}}}$$ axial-vector fields with quantum numbers of $${{J}^{{PC}}} = {{1}^{{ + + }}}$$ and $${{J}^{{PC}}} = {{1}^{{ + - }}}$$, respectively, are taken into account. We demonstrate that the $${{a}_{1}}(1260)$$ and $${{b}_{1}}(1235)$$ do not mix within the SU(2) $$ \times $$ SU(2) chiral scheme. However, a nonzero mixing between the $${{K}_{{1A}}}$$ and $${{K}_{{1B}}}$$ strange axial-vector mesons arises as soon as the strange-quark mass is not equal to those of the u and d quarks, whereby the chiral symmetry is essentially violated. As a result, the $${{K}_{1}}(1270)$$ and $${{K}_{1}}(1400)$$ mesons emerge as physical states. These are taken into account when formulating the additional renormalization of the kaon field.

Axial Vector-Meson–Nucleon Interaction Constant in the AdS/QCD Soft Wall Model

This work investigates the interaction of an axial vector-meson with nucleons in the AdS/QCD soft wall model. The axial vector fields have been determined inside the anti-de Sitter (AdS) space with the help of gauge fields with left and right chiral symmetries. In addition, a pseudoscalar field has been introduced inside the AdS space to break the chiral symmetry. A Lagrangian for these fields has been introduced inside the AdS space and the profile functions which are solutions of the equation of motion have been found. In accordance with AdS/CFT, the interaction constant of the axial vector-meson with the nucleons has been obtained as an integral over the additional dimension. The main task of this work was to find numerical values of the interaction constant of the axial vector-meson with the nucleons in the AdS/QCD soft wall model. With the help of the computer program Mathematica 7, these values were determined. A comparison of the theoretical and experimental data has revealed significant agreement of the results.

Quantum kinetic equation in the rotating frame and chiral kinetic theory

A modified quantum kinetic equation which takes account of the noninertial features of rotating frame is proposed. The vector and axial-vector field components of the Wigner function for chiral fluids are worked out in a semiclassical scheme. It is demonstrated that the chiral currents and energy-momentum tensor computed by means of them are consistent with the hydrodynamical results. A new semiclassical covariant chiral transport equation is established by inspecting the equations satisfied by the chiral vector fields. It uniquely provides a new three-dimensional semiclassical chiral kinetic theory possessing a Coriolis force term. The particle number and current densities deduced from this transport equation satisfy the anomalous continuity equation and generate the magnetic and vortical effects correctly.

Chiral magnetic effect in the presence of an external axial-vector field

We study the excitation of the electric current of chiral fermions along the external magnetic field, known as the chiral magnetic effect, in the presence of the background axial-vector field. The calculation of the current is based on the exact solution of the Dirac equation for these fermions accounting for the external fields. First, this solution was obtained for massive particles and, then, we consider the chiral limit, which is used in the anomalous current computation. We obtain that, in this situation, the anomalous current does not contain the direct contribution of the axial-vector field. This result is compared with findings of other authors.