Component Of Gauge Field Research Articles

Nambu-Goldstone modes in magnetized T2n extra dimensions

We consider a U(1) gauge theory on M4×T4 with background magnetic fluxes. We show that a theory including arbitrary fluxes can always be studied in a theory involving only diagonal fluxes by appropriate coordinate transformations. It is found that the number of independent magnetic fluxes is equal to the rank of the classical value of the field strength matrix, rank⟨F⟩. The number of massless zero modes induced from extra components of higher-dimensional gauge field (Wilson-line scalar field) is also determined by rank⟨F⟩. We explicitly confirm that the quantum corrections due to the matter fermion to the squared mass of the Wilson-line scalar field cancel out at the one-loop level. For this purpose, we derive the fermion mass spectrum on M4×T4 with arbitrary fluxes. By taking the flux diagonal basis, creation and annihilation operators for Kaluza-Klein quantum numbers are defined appropriately. Our results are easily generalized to the case of M4×T2n(n≥3). Published by the American Physical Society 2024

Gauge CPT: A review and use in constructing new affine connections

In this paper, we review the gauge theory of CPT transformations. Even though it may seem absurd to entertain the notion of gauging a discrete symmetry because there are no continuous parameters, we show otherwise via a “back door”. We also make use of the components of the new gauge field [Formula: see text] which are an extension of the metric spin connection to construct various affine connections.

Scalar propagator in a background gluon field beyond the eikonal approximation

We investigate the path integral representation of the scalar propagator in a background gluon field, extending beyond the eikonal approximation by considering all gauge field components and incorporating its x− dependence. Utilizing the worldline formalism, we integrate the Schwinger proper time to express the scalar propagator in light-cone coordinates, facilitating a direct comparison with known results in the literature. The derived propagator captures the change of longitudinal momentum of the projectile within the medium. In the high-energy limit, our result simplifies to the effective gluon propagator employed in the BDMPS-Z formalism. Hence, we propose that our outcome serves as a foundational point for investigating corrections to the BDMPS-Z spectrum arising from the longitudinal momentum transfer of the radiated gluon with the medium, as well as for studying collisional energy loss phenomena. Lastly, by employing an expansion around the classical saddle point solution, we systematically derive an eikonal expansion in inverse powers of the boost parameter, encompassing corrections related to longitudinal momentum transfer and interactions of the projectile with the transverse component of the field.

Dark Grand Unification in the axiverse: decaying axion dark matter and spontaneous baryogenesis

The quantum chromodynamics axion with a decay constant near the Grand Unification (GUT) scale has an ultralight mass near a neV. We show, however, that axion-like particles with masses near the keV–PeV range with GUT-scale decay constants are also well motivated in that they naturally arise from axiverse theories with dark c gauge groups. We demonstrate that the correct dark matter abundance may be achieved by the heavy axions in these models through the misalignment mechanism in combination with a period of early matter domination from the long-lived dark glueballs of the same gauge group. Heavy axion dark matter may decay to two photons, yielding mono-energetic electromagnetic signatures that may be detectable by current or next-generation space-based telescopes. We project the sensitivity of next-generation telescopes including Athena, AMEGO, and e-ASTROGAM to such decaying axion dark matter. If the dark sector contains multiple confining gauge groups, then the observed primordial baryon asymmetry may also be achieved in this scenario through spontaneous baryogenesis. We present explicit orbifold constructions where the dark gauge groups unify with the SM at the GUT scale and axions emerge as the fifth components of dark gauge fields with bulk Chern-Simons terms.

Axial-Vector Form Factor of Nucleons in the Isospin Medium from the Hard-Wall AdS/QCD Model

We study the axial-vector form factor of the nucleons in a constant and homogenous isospin chemical potential using holographic QCD. Nucleon mass splitting in such an isospin medium is taken into account. According to AdS/CFT correspondence, the critical value of the isospin chemical potential equals to UV- boundary value of the time component of the bulk gauge field. We calculate the axial-vector form factor of the proton and neutron in such background in the framework of the hard-wall model and plot the form factors for the isospin chemical potential critical value.

Early dark energy from a higher-dimensional gauge theory

The Hubble constant estimated from the CMB measurements shows large disagreement with the locally measured value. This inconsistency is called the Hubble tension and is vastly studied in recent years. Early Dark Energy (EDE) gives a few percent contribution to the total energy density of the universe only at an epoch before the recombination, and it is considered as a promising solution to the tension. A simple realization of EDE is given by dynamics of a scalar field, called the EDE scalar, and models including the EDE scalar are extensively studied in the literature. In this paper, we present a novel EDE scenario based on higher-dimensional gauge theories. An extra component of gauge fields associated with a compact extra dimension behaves as the EDE scalar at low-energy and has a periodic potential, which has a similar form as potentials for pseudo Nambu-Goldstone bosons (PNGB). In a five-dimensional U(1) gauge theory, we show that a scalar field that originates from the gauge field can give EDE through its dynamics in a PNGB type potential with a suitable choice of parameters in the theory. We focus on the scenario where EDE is explained by the scalar field and clarify constraints on the fundamental parameters of the gauge theory, such as the gauge coupling, the compactification scale, and the mass parameters for matter fields. We also find that a sufficient dilution of EDE requires non-trivial relations among U(1) charges of matter fields. With specific matter contents, we numerically solve the time evolution of the scalar field and confirm that its energy density behaves as an EDE. In our scenario, the parameters of the gauge theory and predicted properties of EDE are related to each other. Thus, the cosmological restrictions on the EDE properties provide insights into higher-dimensional gauge theories.

On the vacuum structure of gauge–Higgs unification models

Abstract We discuss the vacuum structure of the gauge–Higgs unification theory, which is one of the attractive candidates for physics beyond the standard model. This scenario has a remarkable feature: it has infinitely degenerate vacua due to the characteristic periodic potential of the Higgs field, to be identified with the extra space component of the higher-dimensional gauge field. We address the question of whether forming the superposition of such degenerate vacua, like the θ-vacuum in quantum chromodynamics (QCD), is necessary or not, in order to realize the true vacuum state of the theory. We derive a gauge field configuration which describes the transition between neighboring vacua, like the instanton (or anti-instanton) solution in QCD, and the corresponding Euclidean action in two models. In a simplified two-dimensional U(1) model, the derived configuration to describe the transition is shown to have finite Euclidean action, and accordingly the “θ-vacuum” and the resultant “θ-term” are formulated. In a realistic five-dimensional U(1) model, however, the gauge field configuration to describe the transition is shown to have infinite Euclidean action, and therefore the tunneling probability between the degenerate vacua vanishes. Thus, superposition of the degenerate vacua is not necessary.

Erratum: Pseudogauge field driven acoustoelectric current in two-dimensional hexagonal Dirac materials [Phys. Rev. B 105 , 125407 (2022)

Using a diagrammatic scheme, we study the acoustoelectric effects in two-dimensional (2D) hexagonal Dirac materials due to the sound-induced pseudo-gauge field. We analyze both uniform and {\em spatially dispersive} currents in response to copropagating and counterpropagating sound waves, respectively. In addition to the longitudinal acoustoelectric current, we obtain an exotic {\em transverse} charge current flowing perpendicular to the sound propagation direction owing to the interplay of transverse and longitudinal gauge field components $j_T\propto A_L A^\ast_T$. In contrast to the almost isotropic directional profile of the longitudinal uniform current, a highly anisotropic transverse component $j_T\sim\sin(6\theta)$ is achieved that stems from the inherited three-fold symmetry of the hexagonal lattice. However, both longitudinal and transverse parts of the dispersive current are predicted to be strongly anisotropic $\sim\sin^2(3\theta)$ or $\cos^2(3\theta)$. We quantitatively estimate the pseudogauge field contribution to the acoustoelectric current that can be probed in future experiments in graphene and other 2D hexagonal Dirac materials.

Pseudogauge field driven acoustoelectric current in two-dimensional hexagonal Dirac materials

Using a diagrammatic scheme, we study the acoustoelectric effects in two-dimensional (2D) hexagonal Dirac materials due to the sound-induced pseudogauge field. We analyze both uniform and spatially dispersive currents in response to copropagating and counterpropagating sound waves, respectively. In addition to the longitudinal acoustoelectric current, we obtain an exotic transverse charge current flowing perpendicular to the sound propagation direction owing to the interplay of transverse and longitudinal gauge field components ${j}_{T}\ensuremath{\propto}{A}_{L}{A}_{T}^{*}$. In contrast to the almost isotropic directional profile of the longitudinal uniform current, a highly anisotropic transverse component ${j}_{T}\ensuremath{\sim}sin(6\ensuremath{\theta})$ is achieved that stems from the inherited threefold symmetry of the hexagonal lattice. However, both longitudinal and transverse parts of the dispersive current are predicted to be strongly anisotropic $\ensuremath{\sim}{sin}^{2}(3\ensuremath{\theta})$ or ${cos}^{2}(3\ensuremath{\theta})$. We quantitatively estimate the pseudogauge field contribution to the acoustoelectric current that can be probed in future experiments in graphene and other 2D hexagonal Dirac materials.

Gauge symmetry restoration by Higgs condensation in flux compactifications on coset spaces

Extra-dimensional components of gauge fields in higher-dimensional gauge theories will play a role of the Higgs field and become tachyonic after Kaluza-Klein compactifications on internal spaces with (topologically nontrivial) gauge field backgrounds. Its condensation is then expected to break gauge symmetries spontaneously. But, contrary to the expectation, some models exhibit restoration of gauge symmetries. In this paper, by considering all the massive Kaluza-Klein excitations of gauge fields, we explicitly show that some of them indeed become massless at the minimum of the Higgs potential and restore (a part of) the gauge symmetries which are broken by gauge field backgrounds. We particularly consider compactifications on ${S}^{2}$ with monopolelike fluxes and also on ${\mathbb{CP}}^{2}$ with instanton and monopolelike fluxes. In some cases, the gauge symmetry is fully restored, as argued in previous literatures. In other cases, there is a stable vacuum with a partial restoration of the gauge symmetry after Higgs condensation. Topological structure of the gauge field configurations prevent the gauge symmetries from being restored.

Spinning solutions for the bosonic M2-brane with C± fluxes

In this work we obtain classical solutions of the bosonic sector of the supermembrane theory with two-form fluxes associated to a quantized constant C± background. This theory satisfies a flux condition on the worldvolume that induces monopoles over it. Classically it is stable as it does not contain string-like spikes with zero energy in distinction with the general case. At quantum level the bosonic membrane has a purely discrete spectrum but the relevance is that the same property holds for its supersymmetric spectrum. We find for this theory spinning membrane solutions, some of them including the presence of a non-vanishing symplectic gauge connection defined on its worldvolume in different approximations. By using the duality found between this theory and the so-called supermembrane with central charges, rotating membrane solutions found in that case, are also solutions of the M2-brane with C± fluxes. We generalize this result to other embeddings. We find new distinctive rotating membrane solutions, some of them including the presence of a non-vanishing symplectic gauge connection defined on its worldvolume. We obtain numerical and analytical solutions in different approximations characterizing the dynamics of the membrane with fluxes C± for different ansätze of the dynamical degrees of freedom. Finally we discuss the physical admissibility of some of these ansätze to model the components of the symplectic gauge field.

OUP accepted manuscript

Abstract We discuss a natural scenario to solve the strong CP problem in the framework of the higher dimensional gauge theory. An axion-like field Ay has been built-in as the extra-space component of the higher dimensional gauge field. The coupling of Ay with gluons is attributed to the radiatively induced “Chern-Simons” (CS) term. We adopt a toy model with some unknown gauge symmetry U(1)X. The CS term is obtained in two ways: first by a concrete 1-loop calculation and next by use of the Fujikawa’s method to deal with the chiral anomaly in 4D space-time. The obtained results are identical, which implies that the radiative correction to the CS term is “1-loop exact” and is also free from UV-divergence even though the theory itself is non-renormalizable. As a novel feature of this scenario, such obtained CS term is no longer linear in the field Ay as in the usually discussed CS term in 5D space-time but a periodic function of Ay, since Ay has a physical meaning as the Wilson-loop phase. We argue how such novel feature of this scenario causes the modification of the ordinary solutions of the strong CP problem based on the axion fields.

Extranatural flux inflation

We propose a new inflation scenario in flux compactification, where a zero mode scalar field of extra components of the higher dimensional gauge field is identified with an inflaton. The scalar field is a pseudo Nambu-Goldstone boson of spontaneously broken translational symmetry in compactified spaces. The inflaton potential is non-local and finite, which is protected against the higher dimensional non-derivative local operators by quantum gravity corrections thanks to the gauge symmetry in higher dimensions and the shift symmetry originated from the translation in extra spaces. We give an explicit inflation model in a six dimensional scalar QED, which is shown to be consistent with Planck 2018 data.

Gauge invariant canonical symplectic algorithms for real-time lattice strong-field quantum electrodynamics

A class of high-order canonical symplectic structure-preserving geometric algorithms are developed for high-quality simulations of the quantized Dirac-Maxwell theory based strong-field quantum electrodynamics (SFQED) and relativistic quantum plasmas (RQP) phenomena. With minimal coupling, the Lagrangian density of an interacting bispinor-gauge fields theory is constructed in a conjugate real fields form. The canonical symplectic form and canonical equations of this field theory are obtained by the general Hamilton’s principle on cotangent bundle. Based on discrete exterior calculus, the gauge field components are discreted to form a cochain complex, and the bispinor components are naturally discreted on a staggered dual lattice as combinations of differential forms. With pull-back and push-forward gauge covariant derivatives, the discrete action is gauge invariant. A well-defined discrete canonical Poisson bracket generates a semi-discrete lattice canonical field theory (LCFT), which admits the canonical symplectic form, unitary property, gauge symmetry and discrete Poincaré subgroup, which are good approximations of the original continuous geometric structures. The Hamiltonian splitting method, Cayley transformation and symmetric composition technique are introduced to construct a class of high-order numerical schemes for the semi-discrete LCFT. These schemes involve two degenerate fermion flavors and are locally unconditional stable, which also preserve the geometric structures. Admitting Nielsen-Ninomiya theorem, the continuous chiral symmetry is partially broken on the lattice. As an extension, a pair of discrete chiral operators are introduced to reconstruct the lattice chirality. Equipped with statistically quantization-equivalent ensemble models of the Dirac vacuum and non-trivial plasma backgrounds, the schemes are expected to have excellent performance in secular simulations of relativistic quantum effects, where the numerical errors of conserved quantities are well bounded by very small values without coherent accumulation. The algorithms are verified in detail by numerical energy spectra. Real-time LCFT simulations are successfully implemented for the nonlinear Schwinger mechanism induced e-e+ pairs creation and vacuum Kerr effect, where the nonlinear and non-perturbative features captured by the solutions provide a complete strong-field physical picture in a very wide range, which open a new door toward high-quality simulations in SFQED and RQP fields.

’t Hooft–Polyakov Monopole and Instanton-like Topological Solution in Gauge-Higgs Unification

We consider 't Hooft-Polyakov monopole (TPM) as a topological soliton in the 5-dimensional (5D) theory of gauge-Higgs unification. This scenario provides a very natural framework to incorporate the TPM, since the adjoint scalar is builtin as the extra-space component of higher dimensional gauge field. In the process of the analysis, we realize that the condition to be satisfied by the Bogomolny-Prasad-Sommerfield (BPS) state of TPM, the BPS monopole, is equivalent to an (anti-)self-dual condition for the higher dimensional gauge field. This observation, in turn, suggests the presence of instanton-like topological soliton living in the 4D space (including the extra dimension), instead of the 4D space-time in the case of ordinary instanton, say "space-like instanton" with finite energy, instead of finite action. We construct the field configuration for the space-like instanton and calculate its mass, handled by the compactification scale. Next we discuss the BPS monopole, as an anti-self-dual gauge field. We start by constructing a hedgehog-type solution as what is obtained by a local gauge transformation from a trivial vacuum. We also argue in some detail that the relation between these two types of topological solitons becomes manifest through the unified description by use of the ansatz adopted by 't Hooft.

Heavy baryons in holographic QCD with higher dimensional degrees of freedom

We try to introduce heavy flavors to Sakai-Sugimoto model by regarding higher dimensional components of gauge fields as heavy mesons. Using the Forg\'acs and Manton approach, we obtain a theory composed of heavy mesons and the instanton of light flavors. Applying the collective coordinate quantization method, we derived a mass formula of heavy baryons. In the leading order of $1/m_{H}$ expansion ($m_{H}$ the mass of a heavy quark), we find singlet and doublet states in the heavy quark symmetry (HQS). Also, we obtain the degenerate Roper like and odd parity excitations. By virtue of heavy meson degrees of freedom, our mass formula reproduces the mass ordering of $\Sigma^*_c$ and $\Lambda_c^*$ correctly.

Large field excursions from dimensional (de)construction

An inflation model based on dimensional (de)construction of a massive gauge theory is proposed. The inflaton in this model is the “zero-mode” of a component of the massive gauge field in the (de)constructed extra dimensions. The inflaton potential originates from the gauge invariant Stueckelberg potential. At low energy, the field range of the inflaton is enhanced by a factor Nd/2 compared to the field range of the original fields in the model, where d is the number of the (de)constructed extra dimensions and N is the number of the lattice points in each (de)constructed dimension. This enhancement of the field range is used to achieve a trans-Planckian inflaton field excursion. The extension of the mechanism “excursions through KK modes” to the case of (de)constructed extra dimensions is also studied. The burst of particle productions by this mechanism may have observable consequences in a region of the model parameter space.

On plasmon contribution to the hot A0 condensate

In SU(2) gluodynamics, the Debye gluon contribution WD(A0) to the effective action of the temporal gauge field component (we consider A0 = const) in the background Rξext is calculated at high temperaturegauge. It is shown that at A0 ≠ 0 the standard definition k0 = 0 , |k| → 0 corresponds to long distance correlations for the longitudinal in internal space gluons. The transversal gluons become screened by the A0 background field. Therefore, they give zero contributions and have to be excluded from the correlation corrections. The total effective action accounting for the one-loop, two-loop, and correct WD(A0) satisfies Nielsen’s identity that proves gauge invariance of the A0 condensation phenomenon.

A warped relaxion

We construct a UV completion of the relaxion in a warped extra dimension. We identify the relaxion with the zero mode of the fifth component of a bulk gauge field and show how hierarchically different decay constants for this field can be achieved by different localizations of anomalous terms in the warped space. This framework may also find applications for other axion-like fields. The cutoff of the relaxion model is identified as the scale of the IR brane where the Higgs lives, which can be as high as 106 GeV, while above this scale warping takes over in protecting the Higgs mass.

General continuum clockwork

The continuum clockwork is an extra-dimensional set-up to realize certain features of the clockwork mechanism generating exponentially suppressed or hierarchical couplings of light particles. We study the continuum clockwork in a general scheme in which large volume, warped geometry, and localization of zero modes in extra dimension are described by independent parameters. For this, we propose a generalized 5-dimensional linear dilaton model which can realize such set-up as a solution of the model, and examine the KK spectrum and the couplings of zero modes and massive KK modes to boundary-localized operators for the bulk graviton, Abelian gauge bosons and periodic scalar fields. We discuss how those KK spectra and couplings vary as a function of the volume, warping and localization parameters, and highlight the behavior in the parameter region corresponding to the clockwork limit. We discuss also the field range of 4-dimensional axions originating from either 5-dimensional periodic scalar field or the 5-th component of an Abelian gauge field, and comment on the limitations of continuum clockwork compared to the discrete clockwork.