Spinor Matter Research Articles

Pressure from the vacuum of confined spinor matter

Charged spinor matter field is quantized in a spatial region bounded by two parallel neutral plates. The most general set of boundary conditions ensuring the confinement of matter within the plates is considered. We study a response of the vacuum of the confined matter to the background uniform magnetic field which is directed orthogonally to the plates. It is proven that, in the case of a sufficiently strong magnetic field, the vacuum pressure onto the plates is positive and independent of the boundary condition, as well as of the distance between the plates.

A discussion on the most general torsion-gravity with electrodynamics for Dirac spinor matter fields

We consider the most general torsional completion of gravitation together with electrodynamics for the Dirac spinorial material fields, and we show that consistency arguments constrain torsion to be completely antisymmetric and the dynamics to be parity-invariant and described by actions that are either least-order derivative or renormalizable.

QED as the tensionless limit of the spinning string with contact interaction

QED with spinor matter is argued to correspond to the tensionless limit of spinning strings with contact interactions. The strings represent electric lines of force with charges at their ends. The interaction is constructed from a delta-function on the world-sheet which, although off-shell, decouples from the world-sheet metric. Integrating out the string degrees of freedom with fixed boundary generates the super-Wilson loop that couples spinor matter to electromagnetism in the world-line formalism. World-sheet and world-line, but not spacetime, supersymmetry underpin the model.

Casimir effect with quantized charged spinor matter in background magnetic field

We study the influence of a background uniform magnetic field and boundary conditions on the vacuum of a quantized charged spinor matter field confined between two parallel neutral plates; the magnetic field is directed orthogonally to the plates. The admissible set of boundary conditions at the plates is determined by the requirement that the Dirac Hamiltonian operator be self-adjoint. It is shown that, in the case of a sufficiently strong magnetic field and a sufficiently large separation of the plates, the generalized Casimir force is repulsive, being independent of the choice of a boundary condition, as well as of the distance between the plates. The detection of this effect seems to be feasible in the foreseeable future.

Delta-function interactions for the bosonic and spinning strings and the generation of Abelian gauge theory

We construct contact interactions for bosonic and spinning strings. In the tensionless limit of the spinning string this reproduces the super-Wilson loop that couples spinor matter to Abelian gauge theory. Adding boundary terms that quantise the motion of charges results in a string model equivalent to spinor QED. The strings represent lines of electric flux connected to the charges. The purely bosonic model is spoilt by divergences that are excluded from the spinning model by world-sheet supersymmetry, indicating a preference for spinor matter.

Elliptic Hypergeometry of Supersymmetric Dualities II. Orthogonal Groups, Knots, and Vortices

We consider Seiberg electric-magnetic dualities for 4d $\mathcal{N}=1$ SYM theories with SO(N) gauge group. For all such known theories we construct superconformal indices (SCIs) in terms of elliptic hypergeometric integrals. Equalities of these indices for dual theories lead both to proven earlier special function identities and new conjectural relations for integrals. In particular, we describe a number of new elliptic beta integrals associated with the s-confining theories with the spinor matter fields. Reductions of some dualities from SP(2N) to SO(2N) or SO(2N+1) gauge groups are described. Interrelation of SCIs and the Witten anomaly is briefly discussed. Possible applications of the elliptic hypergeometric integrals to a two-parameter deformation of 2d conformal field theory and related matrix models are indicated. Connections of the reduced SCIs with the state integrals of the knot theory, generalized AGT duality for (3+3)d theories, and a 2d vortex partition function are described.

GUT theories from Calabi-Yau 4-folds with SO(10) singularities

We consider an SO(10) GUT model from F-theory compactified on an elliptically fibered Calabi-Yau with a D5 singularity. To obtain the matter curves and the Yukawa couplings, we use a global description to resolve the singularity. We identify the vector and spinor matter representations and their Yukawa couplings and we explicitly build the G-fluxes in the global model and check the agreement with the semi-local results. As our bundle is of type SU(2k), some extra conditions need to be applied to match the fluxes.

Dark energy simulacrum in nonlinear electrodynamics

Quasi-constant external fields in nonlinear electromagnetism generate a contribution to the energy-momentum tensor with the form of dark energy. To provide a thorough understanding of the origin and strength of the effects, we undertake a complete theoretical and numerical study of the energy-momentum tensor $T^{\mu\nu}$ for nonlinear electromagnetism. The Euler-Heisenberg nonlinearity due to quantum fluctuations of spinor and scalar matter fields is considered and contrasted with the properties of classical nonlinear Born-Infeld electromagnetism. We also address modifications of charged particle kinematics by strong background fields.

Dark energy model with spinor matter and its quintom scenario

A class of dynamical dark energy models, dubbed spinor quintom, can be constructed by a spinor field ψ with a nontraditional potential. We find that, if choosing suitable potential, this model is able to allow the equation-of-state to cross the cosmological constant boundary without introducing any ghost fields. In a further investigation, we show that this model is able to mimic a perfect fluid of Chaplygin gas with p = −c/ρ during the evolution, and also realizes the quintom scenario with its equation-of-state across −1.

The Bullough–Dodd model coupled to matter fields

The Bullough–Dodd model is an important two-dimensional integrable field theory which finds applications in physics and geometry. We consider a conformally invariant extension of it, and study its integrability properties using a zero curvature condition based on the twisted Kac–Moody algebra A 2 ( 2 ) . The one- and two-soliton solutions as well as the breathers are constructed explicitly. We also consider integrable extensions of the Bullough–Dodd model by the introduction of spinor (matter) fields. The resulting theories are conformally invariant and present local internal symmetries. All the one-soliton solutions, for two examples of those models, are constructed using a hybrid of the dressing and Hirota methods. One model is of particular interest because it presents a confinement mechanism for a given conserved charge inside the solitons.

Multicomponent gap solitons in spinor Bose-Einstein condensates

We model the nonlinear behaviour of spin-1 Bose-Einstein condensates (BECs) with repulsive spin-independent interactions and either ferromagnetic or anti-ferromagnetic (polar) spin-dependent interactions, loaded into a one-dimensional optical lattice potential. We show that both types of BECs exhibit dynamical instabilities and may form spatially localized multi-component structures. The localized states of the spinor matter waves take the form of vector gap solitons and self-trapped waves that exist only within gaps of the linear Bloch-wave band-gap spectrum. Of special interest are the nonlinear localized states that do not exhibit a common spatial density profile shared by all condensate components, and consequently cannot be described by the single mode approximation (SMA), frequently employed within the framework of the mean-field treatment. We show that the non-SMA states can exhibits Josephson-like internal oscillations and self-magnetisation, i.e. intrinsic precession of the local spin. Finally, we demonstrate that non-stationary states of a spinor BEC in a lattice exhibit coherent undamped spin-mixing dynamics, and that their controlled conversion into a stationary state can be achieved by the application of an external magnetic field.

Fermions in the Ashtekar-Barbero connection formalism for arbitrary values of the Immirzi parameter

The Ashtekar-Barbero-Immirzi formulation of General Relativity is extended to include spinor matter fields. Our formulation applies to generic values of the Immirzi parameter and reduces to the Ashtekar-Romano-Tate approach when the Immirzi parameter is taken equal to the imaginary unit. The dynamics of the gravity-fermions coupled system is described by the Holst plus Dirac action with a non-minimal coupling term. The non-minimal interaction together with the Holst modification to the Hilbert-Palatini action reconstruct the Nieh-Yan invariant, so that the effective action coming out is the one of Einstein-Cartan theory with a typical Fermi-like interaction term: in spite of the presence of spinor matter fields, the Immirzi parameter plays no role in the classical effective dynamics and results to be only a multiplicative factor in front of a total divergence. We reduce the total action of the theory to the sum of dynamically independent Ashtekar-Romano-Tate actions for self and anti-self dual connections, with different weights depending on the Immirzi parameter. This allows to calculate the constraints of the complete theory in a simple way, it is only necessary to realize that the Barbero-Immirzi connection is a weighted sum of the self and anti-self dual Ashtekar connections. Finally the obtained constraints for the separated action result to be polynomial in terms of the self and anti-self dual connections, this could have implications in the inclusion of spinor matter in the framework of non-perturbative quantum gravity.

Quantum Cosmology in the Bruns–Dicke Theory and its Stability

The Bruns–Dicke theory with a scalar field related to the quantum spinor matter is discussed [1]. The quantum Friedmann cosmology is studied. A solution to the equations of motion describing the quantum Friedmann Universe is examined for stability for the case of a flat model of the Universe. A different exact analytical solution to these equations is derived.

Dirac spinor waves and solitons in anisotropic Taub-NUT spaces

We apply a new general method of anholonomic frames with associated nonlinear connection structure to construct new classes of exact solutions of Einstein–Dirac equations in five-dimensional (5D) gravity. Such solutions are parametrized by off-diagonal metrics in coordinate (holonomic) bases or equivalently, by diagonal metrics given with respect to some anholonomic frames (pentads or funfbeins satisfying corresponding constraint relations). We consider two possibilities of generalization of the Taub-NUT metric in order to obtain vacuum solutions of 5D Einstein equations with effective renormalization of constants (by higher dimension anholonomic gravitational interactions) having distinguished anisotropies on an angular parameter or on an extra-dimensional coordinate. The constructions are extended to solutions describing self-consistent propagations of 3D Dirac wave packets in 5D anisotropic Taub-NUT spacetimes. We show that such anisotropic configurations of spinor matter can induce gravitational 3D solitons which are solutions of Kadomtsev–Petviashvili or sine–Gordon equations.

Generalized Hamiltonian dynamicsof Friedmann cosmology with scalar and spinor matter source fields

The classical and quantum dynamics of theFriedmann-Robertson-Walker (FRW) universewith a massless scalar and massive fermionmatter field as a source is discussedwithin the framework of the Diracgeneralized Hamiltonian formalism. TheHamiltonian reduction of this constrainedsystem is realized for two cases of minimaland conformal coupling between gravity andmatter. It is shown that in both cases forall values of curvature,k = 0,±1, of maximally symmetric space there exists atime-independent reduced local Hamiltonian which describes the dynamicsofthe cosmic scale factor. The relevance of conformal timelike Killingvector fields in FRW spacetime to the existence of the time-independentHamiltonian and the corresponding notion of conserved energy isdiscussed. The extended quantization with theWheeler-deWitt equation is compared withthe canonical quantization of unconstrainedsystem. It is shown that quantumobservables treated as expectation valuesof the Dirac observables properly describethe original classical theory.

Dual descriptions of SO(10) supersymmetric gauge theories with arbitrary numbers of spinors and vectors

We examine the low-energy structure of $\mathcal{N}=1$ supersymmetric SO(10) gauge theory with matter chiral superfields in ${N}_{Q}$ spinor and ${N}_{f}$ vector representations. We construct a dual to this model based upon an $\mathrm{SU}{(N}_{f}{+2N}_{Q}\ensuremath{-}7)\ifmmode\times\else\texttimes\fi{}\mathrm{Sp}{(2N}_{Q}\ensuremath{-}2)$ gauge group without utilizing deconfinement methods. This product theory generalizes all previously known Pouliot-type duals to $\mathrm{SO}{(N}_{c})$ models with spinor and vector matter. It also yields large numbers of new dual pairs along various flat directions. The dual description of the SO(10) theory satisfies multiple consistency checks including an intricate renormalization group flow analysis which links it with Seiberg's duality transformations. We discuss its implications for building grand-unified theories that contain all standard model fields as composite degrees of freedom.

More on chiral-nonchiral dual pairs

Expanding upon earlier work of Pouliot and Strassler, we construct chiral magnetic duals to nonchiral supersymmetric electric theories based upon SO(7), SO(8), and SO(9) gauge groups with various numbers of vector and spinor matter superfields. Anomalies are matched and gauge invariant operators are mapped within each dual pair. Renormalization group flows along flat directions are also examined. We find that confining phase quantum constraints in the electric theories are recovered from semiclassical equations of motion in their magnetic counterparts when the dual gauge groups are completely broken down by the Higgs mechanism.

Exact results in SO(11) SUSY gauge theories with spinor and vector matter

We investigate the confining phase vacuum structure of supersymmetric SO(11) gauge theories with one spinor matter field and N f ≤ 6 vectors. We describe several useful tricks and tools that facilitate the analysis of these chiral models and many other theories of similar type. The forms of the N f = 5 and N f = 6 quantum moduli spaces are deduced by requiring that they reproduce known results for SU(5) SUSY QCD along the spinor flat direction. After adding mass terms for vector fields and integrating out heavy degrees of freedom, we also determine the dynamically generated superpotentials in the N f ≤ 4 quantum theories. We close with some remarks regarding magnetic duals to the N f ≥ 7 electric SO(11) theories.

Black holes with Weyl charge and non-Riemannian waves

A simple modification to Einstein's theory of gravity in terms of a non-Riemannian connection is examined. A new tensor-variational approach yields field equations that possess a covariance similar to the gauge covariance of electromagnetism. These equations are shown to possess solutions analogous to those found in the Einstein-Maxwell system. In particular one finds gravi-electric and gravi-magnetic charges contributing to a spherically symmetric static Reissner - Nordström metric. Such Weyl `charges' provide a source for the non-Riemannian torsion and metric gradient fields instead of the electromagnetic field. The theory suggests that matter may be endowed with gravitational charges that couple to gravity in a manner analogous to electromagnetic couplings in an electromagnetic field. The nature of gravitational coupling to spinor matter in this theory is also investigated and a solution exhibiting a plane-symmetric gravitational metric wave coupled via non-Riemannian waves to a propagating spinor field is presented.

THE SPECTRUM OF TOPOLOGICALLY MASSIVE QUANTUM ELECTRODYNAMICS

We discuss the possibility for the spectrum of topologically massive quantum electrodynamics with spinor matter fields to contain unexpected and unusual stable particle excitations for certain values of the topological photon mass. The new field theoretical phenomena arising from this novel spectral structure are briefly discussed.