Component Of Gauge Field Research Articles

The standard model gauge symmetry from higher-rank unified groups in grand gauge-Higgs unification models

We study grand unified models in the five-dimensional space-time where the extra dimension is compactified on S1/ℤ2. The spontaneous breaking of unified gauge symmetries is achieved via vacuum expectation values of the extra-dimensional components of gauge fields. We derive one-loop effective potentials for the zero modes of the gauge fields in SU(7), SU(8), SO(10), and E6 models. In each model, the rank of the residual gauge symmetry that respects the boundary condition imposed at the orbifold fixed points is higher than that of the standard model. We verify that the residual symmetry is broken to the standard model gauge symmetry at the global minima of the effective potential for certain sets of bulk fermion fields in each model.

Polyakov loop in a non-covariant operator formalism

We discuss a Polyakov loop in non-covariant operator formalism which consists of only physical degrees of freedom at finite temperature. It is pointed out that although the Polyakov loop is expressed by a Euclidean time component of gauge fields in a covariant path integral formalism, there is no direct counterpart of the Polyakov loop operator in the operator formalism because the Euclidean time component of gauge fields is not a physical degree of freedom. We show that by starting with an operator which is constructed in terms of only physical operators in the non-covariant operator formalism, the vacuum expectation value of the operator calculated by trace formula can be rewritten into a familiar form of an expectation value of Polyakov loop in a covariant path integral formalism at finite temperature for the cases of axial and Coulomb gauge.

Remarks on the effects of the Gribov copies on the infrared behavior of higher dimensional Yang-Mills theory

In this paper, we discuss non-perturbative infrared features of Yang-Mills theory in Euclidean space-time dimensions greater than four in the Landau gauge and within the Refined Gribov-Zwanziger framework, which enables us to take into account the existence of gauge copies by restricting the domain of integration in the path integral to the Gribov region. Evidences for a decoupling/massive solution for the gluon propagator in higher dimensions are provided. This behavior is strengthened the bigger the dimension is. Further, we show that, by a dimensional reduction of the Refined Gribov-Zwanziger action from five to four dimensions, a non-perturbative coupling between the inverse of the Faddeev-Popov operator and the scalar field corresponding to the fifth component of the gauge field naturally arises, being in agreement with the recently proposed mechanism \cite{Capri:2014bsa} to generalize the Refined Gribov-Zwanziger construction to the matter sector.

Amperean Pairing at the Surface of Topological Insulators.

The surface of a 3D topological insulator is described by a helical electron state with the electron's spin and momentum locked together. We show that in the presence of ferromagnetic fluctuations the surface of a topological insulator is unstable towards a superconducting state with unusual pairing, dubbed Amperean pairing. The key idea is that the dynamical fluctuations of a ferromagnetic layer deposited on the surface of a topological insulator couple to the electrons as gauge fields. The transverse components of the magnetic gauge fields are unscreened and can mediate an effective interaction between electrons. There is an attractive interaction between electrons with momenta in the same direction which makes the pairing to be of Amperean type. We show that this attractive interaction leads to a p-wave pairing instability of the Fermi surface in the Cooper channel.

Gauge and emergent electromagnetic fields for moving magnetic topological solitons

We apply the general concept of non-Abelian gauge fields for the description of magnetic soliton excitations. We show that the component of the gauge field potential along the soliton local magnetization (Abelian part of the gauge potential) determines the dynamics of spin fluctuations over the soliton background in a ferromagnet. The assumption that the gauge field is a pure gauge allows calculating the gauge field components and finding simple expressions for the emergent electromagnet fields related to the soliton motion. The gauge field results in a soliton-magnon interaction leading to renormalization of the soliton and magnon dynamics. The presented approach allows reaching a deeper understanding of the relationship between field theory and condensed-matter magnetism.

Natural millicharged inflation

We construct a natural inflation model with the inflaton as a linear combination of the fifth components of Abelian gauge fields in a five-dimensional theory. A seesaw mechanism is introduced to provide a natural milli-charge for matter fields under one combination of the gauge symmetries. As a result, the effective decay constant of the inflaton field can be above the Planck scale with all scales in the model below the Planck scale. Our model predicts a tensor-to-scalar ratio r between 0.033 and 0.125 for sixty e-folds and a reheating temperature of a few 10^11 GeV.

Higgs bosons in extra dimensions

In this paper, motivated by the recent discovery of a Higgs-like boson at the Large Hadron Collider (LHC) with a mass mH≃125 GeV , we review different models where the hierarchy problem is solved by means of a warped extra dimension. In the Randall–Sundrum (RS) model electroweak observables provide very strong bounds on the mass of KK modes which motivates extensions to overcome this problem. Two extensions are briefly discussed. One particular extension is based on the deformation of the metric such that it strongly departs from the AdS5 structure in the IR region while it goes asymptotically to AdS5 in the UV brane. This model has the IR brane close to a naked metric singularity (which is outside the physical interval) characteristic of soft-walls constructions. The proximity of the singularity provides a strong wave function renormalization for the Higgs field which suppresses the T and S parameters. The second class of considered extensions are based on the introduction of an extra gauge group in the bulk such that the custodial SU (2)R symmetry is gauged and protects the T parameter. By further enlarging the bulk gauge symmetry one can find models where the Higgs is identified with the fifth component of gauge fields and for which the Higgs potential along with the Higgs mass can be dynamically determined by the Coleman–Weinberg mechanism.

The ([formula omitted]) curved Dirac equation in polar coordinates in the presence of electromagnetic field

In this work we study the covariant Dirac equation in (2+1) dimensional space–time in the presence of electromagnetic field. In polar coordinates, we show that by using a unitary transformation which implies a constraint between the components of gauge field, the covariant Dirac equation can be transformed into a Schrodinger-like differential equation for one of the spinor components. We also obtain the relativistic energy and spinor wave function for two different kinds of electrostatic potentials. The non-relativistic limit of the Dirac equation is also studied and it is shown that the upper spinor component satisfies the Pauli equation.

Weyl semimetals with short-range interactions

We construct a low-energy effective field theory of electrons interacting via short-range interactions in a Weyl semimetal and investigate possible broken-symmetry ground states through an unbiased one-loop renormalization group (RG) analysis. Using the symmetries of the noninteracting Weyl semimetal to constrain the form of the interaction term leads to four independent coupling constants. We investigate the stability of RG flows towards strong coupling and find a single stable trajectory. In order to determine the most likely broken-symmetry ground state, we calculate susceptibilities in the particle-hole and particle-particle channels along this trajectory and find that the leading instability is towards a fully gapped spin-density wave (SDW) ground state. The sliding mode of this SDW couples to the external electromagnetic fields like the Peccei-Quinn axion field of particle physics. We also study a maximally symmetric toy model of an interacting Weyl semimetal with a single independent coupling constant. The most likely ground states in this case are either gapless ferromagnetic states where the spin waves couple to the Weyl fermions like the spatial components of a (possibly chiral) gauge field, or a fully gapped spin-singlet Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state.

CP violation from pure gauge in extra dimensions

One of the Sakharov's condition for baryogenesis is the violation of both C and CP. In the Standard Model, gauge interactions break maximally C, but CP is only broken through the Yukawa couplings in the poorly understood scalar sector. In extra-dimensional models, extra components of gauge fields behave as scalars in 4D and can acquire effective vev's through (finite) quantum effects (Hosotani mechanism). This mechanism is used to build a toy model with 2 extra-dimensions compactified on a flat torus $T^2$, where a SU(2) gauge symmetry is broken to U(1) and CP violation (in 4D) is expected. This is verified by computing a non-vanishing electric dipole moment.

Are there infinitely many decompositions of the nucleon spin?

We discuss the uniqueness or non-uniqueness problem of the decomposition of the gluon field into the physical and pure-gauge components, which is the basis of the recently proposed two physically inequivalent gauge-invariant decompositions of the nucleon spin. It is crucialy important to recognize the fact that the standard gauge fixing procedure is essentially a process of projecting out the physical components of the massless gauge field. A complexity of the nonabelian gauge theory as compared with the abelian case is that a closed expression for the physical component can be given only with use of the non-local Wilson line, which is generally path-dependent. It is known that, by choosing an infinitely long straight-line path in space and time, the direction of which is characterized by a constant 4-vector $n^\mu$, one can cover a class of gauge called the general axial gauge, containing three popular gauges, i.e. the temporal, the light-cone, and the spatial axial gauge. Within this general axial gauge, we have calculated the 1-loop evolution matrix for the quark and gluon longitudinal spins in the nucleon. We found that the final answer is exactly the same independently of the choices of $n^\mu$, which amounts to proving the gauge-independence and path-independence simultaneously, although within a restricted class of gauges and paths. By drawing on all of these findings together with well-established knowledge from gauge theories, we argue against the rapidly spreading view in the community that there are infinitely many decompositions of the nucleon spin.

Chern-Simons inflation and baryogenesis

We present a model of inflation based on the interaction between a homogeneous and isotropic configuration of a U(1) gauge field and fermionic charge density \U0001d4a50. The regulated fermionic charge density is generated from a Bunch-Davies vacuum state using the methods of Koksma and Prokopec [11], and is found to redshift as 1/a(η). The time-like component of gauge field is sourced by the fermionic charge leading to a growth in the gauge field A(η)0 ∼ a(η). As a result inflation is dominated by the energy density contained in the gauge field and fermionic charge interaction, A0 \U0001d4a50, which remains constant during inflation. We also provide a mechanism to generate a net lepton asymmetry. The coupling of a pseudo scalar to the Chern-Simons term converts the gauge field fluctuations into lepton number and all three Sahkarov conditions are satisfied during inflation. Finally, the rapid oscillation of the pseudo scalar field near its minimum thermalizes the gauge field and ends inflation. We provide the necessary initial condition on the gauge field and fermionic charge to simultaneously generate enough e-folds and baryon asymmetry index.

GAUGE THEORY ON A SPACE WITH LINEAR LIE TYPE FUZZINESS

The U(1) gauge theory on a space with Lie type noncommutativity is constructed. The construction is based on the group of translations in Fourier space, which in contrast to space itself is commutative. In analogy with lattice gauge theory, the object playing the role of flux of field strength per plaquette, as well as the action, is constructed. It is observed that the theory, in comparison with ordinary U(1) gauge theory, has an extra gauge field component. This phenomena is reminiscent of similar ones in formulation of SU (N) gauge theory in space with canonical noncommutativity, and also appearance of gauge field component in discrete direction of Connes' construction of the Standard Model.

A Lorentz invariant doubled world-sheet theory

We propose a Lorentz invariant version of Tseytlin's doubled worldsheet theory that makes T-duality covariance of the string manifest. This theory can be derived as a gauge fixed version of Buscher's gauging procedure, in which the left-over gauge field component acts as a Lagrange multiplier. This description can naturally account for fractional linear O(D,D) transformations of the metric and b-field. It is capable of describing non-geometric backgrounds; geometric and non-geometric fluxes are encoded in the doubled anti-symmetric tensor field strength.

Holographic superconductors withz=2Lifshitz scaling

We use gauge/gravity duality to explore strongly coupled superconductors with dynamical exponent $z=2$. In the probe limit we numerically establish background solutions for the matter fields and plot the condensate versus the dimensionless temperature. We then investigate electromagnetic perturbations in order to compute the AC conductivity and also calculate the spectral function. Our results for the condensate and conductivity are qualitatively similar to those of the AdS superconductor. However, we find that (for both s- and p-wave) the condensate does not approach a constant at very low temperature and the conductivity goes to one from below but never exceeds it in the high frequency limit, in contrast to the AdS black hole. We do not see a peak at nonzero frequency in the imaginary part of the AC conductivity along the $x$ direction for the p-wave case. These features are due to the nontrivial dynamical exponent. To be specific, the black hole geometry considered in this work is anisotropic between space and time, very different from the Schwarzschild-AdS black hole, which results in different asymptotic behaviors of temporal and spatial components of gauge fields than those in the Schwarzschild-AdS black hole.

Gauge-Higgs unification in Lifshitz-type gauge theory

We discuss the gauge-Higgs unification in a framework of Lifshitz type gauge theory. We study a higher dimensional gauge theory on R^{D-1}\times S^{1} in which the normal second (first) order derivative terms for scalar (fermion) fields in the action are replaced by higher order derivative ones for the direction of the extra dimension. We provide some mathematical tools to evaluate a one-loop effective potential for the zero mode of the extra component of a higher dimensional gauge field and clarify how the higher order derivative terms affect the standard form of the effective potential. Our results show that they can make the Higgs mass heavier and change its vacuum expectation value drastically. Some extensions of our framework are briefly discussed.

Gauge and Lorentz Transformation Placed on the Same Foundation

We show that a “dynamical” interaction for arbitrary spin can be constructed in a straightforward way if gauge and Lorentz transformations are placed on the same foundation. As Lorentz transformations act on space‐time coordinates, gauge transformations are applied to the gauge field. Placing these two transformations on the same ground means that all quantized field like spin‐1/2 and spin‐3/2 spinors are functions not only of the coordinates but also of the gauge field components. As a consequence, on this stage the (electromagnetic) gauge field has to be considered as classical field. Therefore, standard quantum field theory cannot be applied. Despite this inconvenience, such a common ground is consistent with an old dream of physicists almost a century ago. Our approach, therefore, indicates a straightforward way to realize this dream.

A six-dimensional gauge-Higgs unification model based on E 6 gauge symmetry

We construct a six-dimensional gauge-Higgs unification model with the enlarged gauge group of E 6 on S 2 / Z 2 orbifold compactification. The standard model particle contents and gauge symmetry are obtained by utilizing a monopole background field and imposing appropriate parity conditions on the orbifold. In particular, a realistic Higgs potential suitable for breaking the electroweak gauge symmetry is obtained without introducing extra matter or assuming an additional symmetry relation between the SU(2) isometry transformation on the S 2 and the gauge symmetry. The Higgs boson is a KK mode associated with the extra-dimensional components of gauge field. We also compute the KK masses of all fields at tree level.

Fate of non-Fermi-liquid behavior inQED3at finite chemical potential

The damping rate of two-dimensional massless Dirac fermions exhibit non-Fermi liquid behavior, $\propto \epsilon^{1/2}$, due to gauge field at zero temperature and zero chemical potential. We study the fate of this behavior at finite chemical potential. We fist calculate explicitly the temporal and spatial components of vacuum polarization functions. The analytical expressions imply that the temporal component of gauge field develops a static screening length at finite chemical potential while the transverse component remains long-ranged owing to gauge invariance. We then calculate the fermion damping rate and show that the temporal gauge field leads to normal Fermi liquid behavior but the transverse gauge field leads to non-Fermi liquid behavior $\propto \epsilon^{2/3}$ at zero temperature. This energy-dependence is more regular than $\propto \epsilon^{1/2}$ and does not change as chemical potential varies.

Erratum: Collider signatures of the gauge-Higgs dark matter [Phys. Rev. D81, 097703 (2010)

A recently proposed SO(5)xU(1) gauge-Higgs unification model in the Randall-Sundrum warped space contains a very interesting dark matter candidate, the Higgs boson. As a part of the fifth component of a five-dimensional gauge field, the four-dimensional neutral Higgs boson has odd H parity while all the other standard model particles have even parity to all orders in perturbation theory. Based on H-parity conserving WWHH and ZZHH vertices, we investigate the collider signatures of Higgs dark matter production associated with a SM W or Z gauge boson at the LHC and the ILC. The final state consists of a W or a Z boson with large missing energy. We found that the level of the signal cross section is quite hopeless at the LHC while we may be able to identify it at the ILC with polarized electron beams.