Higher Dimensional Gauge Fields 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

Cosmological dynamics of string theory axion strings

The quantum chromodynamics (QCD) axion may solve the strong CP problem and explain the dark matter (DM) abundance of our Universe. The axion was originally proposed to arise as the pseudo-Nambu-Goldstone boson of global U(1)PQ Peccei-Quinn (PQ) symmetry breaking, but axions also arise generically in string theory as zero modes of higher-dimensional gauge fields. In this work we show that string theory axions behave fundamentally differently from field theory axions in the early Universe. Field theory axions may form axion strings if the PQ phase transition takes place after inflation. In contrast, we show that string theory axions do not generically form axion strings. In special inflationary paradigms, such as D-brane inflation, string theory axion strings may form; however, their tension is parametrically larger than that of field theory axion strings. We then show that such QCD axion strings overproduce the DM abundance for all allowed QCD axion masses and are thus ruled out, except in scenarios with large warping. A loop-hole to this conclusion arises in the axiverse, where an axion string could be composed of multiple different axion mass eigenstates; a heavier eigenstate could collapse the network earlier, allowing for the QCD axion to produce the correct DM abundance and also generating observable gravitational wave signals. Published by the American Physical Society 2024

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.

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.

’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.

F-term axion monodromy inflation

The continuous shift symmetry of axions is at the heart of several realizations of inflationary models. In particular, axion monodromy inflation aims at achieving super-Planckian field ranges for the inflaton in the context of string theory. Despite the elegant underlying principle, explicit models constructed hitherto are exceedingly complicated. We propose a new and better axion monodromy inflationary scenario, where the inflaton potential arises from an F-term. We present several scenarios, where the axion arises from the Kaluza-Klein compactification of higher dimensional gauge fields (or p-form potentials) in the presence of fluxes and/or torsion homology. The monodromy corresponds to a change in the background fluxes, and its F-term nature manifests in the existence of domain walls interpolating among flux configurations. Our scenario leads to diverse inflaton potentials, including linear large field behaviour, chaotic inflation, as well as potentials with even higher powers. They provide an elegant set of constructions with properties in the ballpark of the recent BICEP2 observational data on primordial gravitational waves.

Anomalous Higgs interactions in gauge-Higgs unification

We discuss anomalous Higgs interactions in the scenario of gauge-Higgs unification. In the scenario Higgs originates from higher dimensional gauge field and has a physical meaning as AB phase or Wilson loop. As its inevitable consequence, physical observables are expected to be periodic in the Higgs field. In particular, the Yukawa coupling is expected to show some periodic and non-linear behavior as the function of the Higgs VEV. For a specific choice of the VEV, the Yukawa coupling of KK zero mode fermion even vanishes. On the other hand, the Yukawa coupling is originally provided by gauge interaction, which is linear in the Higgs field. We discuss how such two apparent contradiction about the non-linearity of the Yukawa coupling can be reconciled and at the same time how these two "pictures" give different predictions in the simplest framework of the scenario: SU(3) electroweak model in 5-dimensional flat space-time with orbifolding. The deviation of the Yukawa coupling from the standard model prediction is also calculated for arbitrary VEV. We study "$H$-parity", which guarantees the stability of the Higgs for a specific choice of the VEV. Also discussed is the Higgs interaction with $W^\pm$ and $Z^0$. It turns out that in our framework of flat space-time the interaction does not show deviation from the standard model prediction, except for the specific case of the VEV.

Model to localize gauge and tensor fields on thick branes

It is shown that the introduction of a suitable function in the higher-dimensional gauge field action may be used in order to achieve gauge bosons localization on a thick brane. The model is constructed upon analogies to the effective coupling of neutral scalar field to electromagnetic field and to the Friedberg-Lee model for hadrons. After that we move forward studying the localization of the Kalb-Ramond field via this procedure.

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.

Higgs Inflaton Potential in Higher-Dimensional SUSY Gauge Theories

We study the possibility that the Higgs and the inflaton are the same single field or cousins arising from the extra space components of some higher-dimensional gauge field. We take 5D supersymmetric gauge theory with a matter compactified on S as a toy model and evaluate the one-loop contribution to the Higgs-inflaton potential. Our gauge-Higgs-inflaton unification picture applied to the gauge field of intermediate energy scale (∼ 10 GeV) can explain the observed inflation parameters without fine-tuning.

Quartification on an orbifold

We investigate quartification models in five dimensions, with the fifth dimension forming an ${S}^{1}/{Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}^{\ensuremath{'}}$ orbifold. The orbifold construction is combined with a boundary Higgs sector to break the quartified gauge group directly to a group $H\ensuremath{\subset}SU(3{)}^{4}$ which is operative at the electroweak scale. We consider $H={G}_{\mathrm{SM}}\ensuremath{\bigotimes}SU(2{)}_{\ensuremath{\ell}}$ and $H={G}_{\mathrm{SM}}$, where ${G}_{\mathrm{SM}}$ is the standard model gauge group, and find that unification occurs only when the remnant leptonic color symmetry $SU(2{)}_{\ensuremath{\ell}}$ remains unbroken. Furthermore, the demands of a realistic low-energy fermion spectrum specify a unique symmetry breaking route for the unifying case of $H={G}_{\mathrm{SM}}\ensuremath{\bigotimes}SU(2{)}_{\ensuremath{\ell}}$. We contrast this with four-dimensional quartification models where unification may be achieved via a number of different symmetry breaking routes both with and without the remnant $SU(2{)}_{\ensuremath{\ell}}$ symmetry. The boundary Higgs sector of our model may be decoupled to achieve a Higgsless limit, and we show that the electroweak Higgs doublet may be identified as the fifth component of a higher-dimensional gauge field.

Gauge-Higgs unification with brane kinetic terms

By identifying the Higgs field as an internal component of a higher-dimensional gauge field it is possible to solve the little hierarchy problem. The construction of a realistic model that incorporates such a gauge-Higgs unification is an important problem that demands attention. In fact, several attempts in this direction have already been put forward. In this Letter we single out one such attempt, a 6D SU(3) extended electroweak theory, where it is possible to obtain a Higgs mass prediction in accord with global fits. One shortcoming of the model is its prediction for the Weinberg angle, it is too large. We slightly modify the model by including brane kinetic terms in a way motivated by the orbifold action on the 6D fields. We show that in this way it is possible to obtain the correct Weinberg angle while keeping the desired results in the Higgs sector.

QCD axion from a higher dimensional gauge field theory.

We point out that a QCD axion solving the strong CP problem can arise naturally from a parity-odd gauge field in five-dimensional (5D) orbifold field theory. The required axion coupling to the QCD anomaly comes from the 5D Chern-Simons coupling, and all other unwanted U(1)PQ breaking axion couplings can be avoided naturally by the 5D gauge symmetry and locality. If the fifth dimension is warped, the resulting axion scale is suppressed by a small warp factor compared to the Planck scale, thereby the model can generate naturally an intermediate axion scale fa = 10(10)-10(12) GeV.

Standard model Higgs boson from higher dimensional gauge fields

We consider the possibility that the standard model Higgs fields may originate from extra components of higher dimensional gauge fields. Theories of this type considered before have had problems accommodating the standard model fermion content and Yukawa couplings different from the gauge coupling. Considering orbifolds based on Abelian discrete groups we are led to a 6 dimensional ${G}_{2}$ gauge theory compactified on ${T}^{2}{/Z}_{4}.$ This theory can naturally produce the SM Higgs fields with the right quantum numbers while predicting the value of the weak mixing angle ${\mathrm{sin}}^{2}{\ensuremath{\theta}}_{W}=0.25$ at the tree level, close to the experimentally observed one. The quartic scalar coupling for the Higgs boson is generated by the higher dimensional gauge interaction and predicts the existence of a light Higgs boson. We point out that one can write a quadratically divergent counterterm for Higgs boson mass localized to the orbifold fixed point. However, we calculate these operators and show that higher dimensional gauge interactions do not generate them at least at one loop. Fermions are introduced at orbifold fixed points, making it easy to accommodate the standard model fermion content. Yukawa interactions are generated by Wilson lines. They may be generated by the exchange of massive bulk fermions, and the fermion mass hierarchy can be obtained. Around a TeV, the first KK modes would appear as well as additional fermion modes localized at the fixed point needed to cancel the quadratic divergences from the Yukawa interactions. The cutoff scale of the theory could be a few times 10 TeV.

Unification of Higgs and gauge fields in five dimensions

We construct realistic theories in which the Higgs fields arise from extra-dimensional components of higher-dimensional gauge fields. In particular, we present a minimal 5D SU(3) C × SU(3) W model and a unified 5D SU(6) model. In both cases the theory is reduced to the minimal supersymmetric standard model below the compactification scale, with the two Higgs doublets arising from the 5D gauge multiplet. Quarks and leptons are introduced in the bulk, giving Yukawa couplings without conflicting with higher-dimensional gauge invariance. Despite the fact that they arise from higher-dimensional gauge interactions, the sizes of these Yukawa couplings can be different from the 4D gauge couplings due to wave-function profiles of the matter zero modes determined by bulk mass parameters. All unwanted fields are made heavy by introducing appropriate matter and superpotentials on branes, which are also the source of intergenerational mixings in the low-energy Yukawa matrices. The theory can accommodate a realistic structure for the Yukawa couplings as well as small neutrino masses. Scenarios for supersymmetry breaking and the μ-term generation are also discussed.

Vector field localization and negative tension branes

It is shown that negative tension branes in higher dimensions may lead to an effective lower dimensional theory where the gauge-invariant vector fields associated with the fluctuations of the metric are always massless and localized on the brane. Explicit five-dimensional examples of this phenomenon are provided. Furthermore, it is shown that higher dimensional gauge fields can also be localized on these configurations with the zero mode separated from the massive tower by a gap.

Massive higher dimensional gauge fields as messengers of supersymmetry breaking

We consider theories with one or more compact dimensions with size r > 1/M, where M is the fundamental Planck scale, with the visible and hidden sectors localized on spatially separated "3-branes." We show that a bulk U(1) gauge field spontaneously broken on the hidden-sector 3-brane is an attractive candidate for the messenger of supersymmetry breaking. In this scenario scalar mass-squared terms are proportional to U(1) charges, and therefore naturally conserve flavor. Arbitrary flavor violation at the Planck scale gives rise to exponentially suppressed flavor violation at low energies. Gaugino masses can be generated if the standard gauge fields propagate in the bulk; \mu and B\mu terms can be generated by the Giudice-Masiero or by the VEV of a singlet in the visible sector. The latter case naturally solves the SUSY CP problem. Realistic phenomenology can be obtained either if all microscopic parameters are order one in units of M, or if the theory is strongly coupled at the scale M. (For the latter case, we estimate parameters by extending "naive dimensional analysis" to higher-dimension theories with branes.) In either case, the only unexplained hierarchy is the "large" size of the extra dimensions in fundamental units, which need only be an order of magnitude. All soft masses are naturally within an order of magnitude of m_{3/2}, and trilinear scalar couplings are negligible. Squark and slepton masses can naturally unify even in the absence of grand unification.

On linear systems and higher dimensional gauge fields

Complete solvability of a linear system corresponds in a certain case to a particular reduction of the gauge group SO(4n) to Sp(1)× Sp(n) Z 2 . This leads to a local classification theorem of certain holomorphic bundles on CP 2 n+1 .