non-Abelian Structure Research Articles

Non-Abelian Landau-Ginzburg theory of ferromagnetic superconductivity and mixing between U(1) and SU(2) gauge bosons

We propose an effective theory of non-Abelian superconductivity, an SU(2)xU(1) extension of the Abelian Landau-Ginzburg theory, which could be viewed as an effective theory of ferromagnetic superconductivity made of spin-up and spin-down doublet Cooper pair. Just like the Abelian Landau-Ginzburg theory it has the U(1) electromagnetic interaction, but the new ingredient is the non-Abelian SU(2) gauge interaction between the spin doublet Cooper pairs. A remarkable feature of the theory is the mixing between the U(1) gauge boson and the diagonal part of the SU(2) gauge boson. After the mixing it has a massless non-Abelian gauge boson (the massless s-boson) and massive gauge boson (the massive photon), in addition to the massive off-diagonal non-Abelian gauge bosons (the massive s-bosons) which induce the spin-flip interaction between the spin up and down components of the Cooper pair. So, unlike the ordinary Landau-Ginzburg theory it has a long range interaction mediated by the massless s-boson, which could be responsible for the long range magnetic order and spin waves observed in ferromagnetic superconductors. The theory is characterized by three scales. In addition to the correlation length fixed by the mass of the Higgs field it has two different penetration lengths, the one fixed by the mass of the photon (which generates the well known Meissner effect) and the other fixed by the mass of the off-diagonal gauge bosons (which determines the range of the spin flip interaction). The non-Abelian structure of the theory naturally accommodates new topological objects, the non-Abrikosov quantized spin vortex (as well as the well known Abrikosov vortex) and non-Abelian spin monopole. We discuss the physical implications of the non-Abelian Landau-Ginzburg theory.

Non-Abelian gauge structure and flavor mixing in quantum field theory1

The quantum field theory formalism describing the phenomenon of neutrino mixing and oscillations is reviewed in its essential aspects. The condensate structure of the flavor vacuum state is considered and its non-perturbative nature is discussed within the existence in the quantum field theory of the manifold of unitarily inequivalent representations of the anticommutation relations. The Poincaré structure of the theory is discussed in connection with the gauge theory features of neutrino mixing, where the possibility arises to describe flavored neutrinos as on-shell fields with definite masses. The flavor vacuum state may be thought of as a refractive medium where different refraction indexes are related to the different neutrino masses. Neglecting the condensate structure of the flavor vacuum implies neglecting second-order contributions in the gauge field coupling and leads to experimentally inconsistent results.

Bounds on anomalous quartic WWZγ couplings in e – p collisions at the FCC-he

Non-Abelian structure of the standard model (SM) predicts the self-interactions of gauge bosons triple gauge couplings (TGC) and quartic gauge couplings (QGC). On the other hand, it is also important to determine the deviations from SM via anomalous triple gauge couplings and anomalous quartic gauge couplings (aQGC) to test the nature of the SM and to see the effects of new physics arising from the beyond the standard model. In this study, we focus on the e − p → jZ γ ν e → j(l + l −)γ ν e process to examine the WWZ γ aQGC at the Future Circular Collider-hadron electron with center-of-mass energy TeV using a model-independent way in the effective theory approach. A Cut-based method is applied to analyse the signal and relevant SM background. Using the total cross-sections, we constrained the anomalous f T,i=0,1,2,5,6,7/Λ4 couplings arising from dimension-8 operators at 95% confidence level for the dilepton decay of the Z-boson. The results are composed of integrated luminosities of and 3 ab −1 under the systematic uncertainties of 0%, 5% and 10%. In the calculations, we use the form factor to eliminate the effects of the violation of unitarity. With this, we obtained the limits for the energy scale of the form factor Λ = 1 TeV. In addition to all this, we use the advantages of ep collisions for analysing the process with much cleaner environment and lower background effects compared with the pp collisions. The obtained sensitivities on f T, i=0, 1, 2, 5, 6, 7/Λ4 are comparable with the experimental results and related phenomenological studies in the literature.

Orbital Hall effect in bilayer transition metal dichalcogenides: From the intra-atomic approximation to the Bloch states orbital magnetic moment approach

Using an effective Dirac model, we study the orbital Hall effect (OHE) in bilayers of transition metal dichalcogenides with 2H stacking (2H-TMD). We use first-order perturbation theory in the interlayer coupling of the bilayer system to obtain analytical expressions for the orbital Hall conductivity in the linear response regime. We use two distinct descriptions of the orbital angular momentum (OAM) operator. The first one is the intra-atomic approximation that considers only the intrasite contribution to the OAM [Cysne et al., Phys. Rev. Lett. 126, 056601 (2021)]. The second one uses the Berry phase formula of the orbital (valley) magnetic moment to describe the OAM operator [Bhowal and Vignale, Phys. Rev. B 103, 195309 (2021)]. This approach includes both intersite and intrasite contributions to the OAM. Our results suggest that the two approaches agree qualitatively in describing the OHE in bilayers of 2H-TMDs, although they present some quantitative differences. We also show that interlayer coupling plays an essential role in understanding the OHE in the unbiased bilayer of 2H-TMD. This coupling causes the Bloch states to become bonding (antibonding) combinations of states of individual layers, demanding the consideration of the non-Abelian structure of the orbital magnetic moment to the occurrence of OHE. As we discuss throughout the work, the emerging picture of transport of OAM in the unbiased bilayer of 2H-TMDs based on OHE is very different from the usual picture based on the valley Hall effect, shedding new light on previous experimental results. We also discuss the effect of the inclusion of a gate-voltage bias in the bilayer system. Our work gives support to recent theoretical predictions on OHE in two-dimensional materials.

Search for the anomalous ZZγ and Zγγ couplings via ννγ production at the CLIC

The non-Abelian gauge structure of the Standard Model implies the presence of the multi-boson self-interactions. Precise measurements in experimental and theoretical studies of these interactions allow not only testing the nature of the Standard Model but also new physics contribution coming from the beyond Standard Model. These interactions can be examined using a model-independent way in effective theory approach that composes the motivation part of this study. In this paper, we examine the anomalous ZZγ and Zγγ neutral triple gauge couplings via the process e−e+→Zγ for the neutrino-antineutrino pair decay of Z boson. It has performed with both unpolarized and polarized electron beams at the Compact Linear Collider with s=3 TeV. The study focused on CP-conserving CB˜W/Λ4 and CP-violating CBB/Λ4, CBW/Λ4, CWW/Λ4 couplings. Obtained sensitivities on the anomalous neutral triple gauge couplings with 95% Confidence Level are given with systematic uncertainties of 0%, 5% and 10% for unpolarized, −80% and 80% polarized electron beams with integrated luminosities of Lint=5ab−1, Lint=4ab−1 and Lint=1ab−1, respectively. Comparing the latest experimental limits and related phenomenological studies, our results on the anomalous neutral gauge couplings are set more stringent sensitivity between 10-30 times of magnitude.

Axions, higher-groups, and emergent symmetry

Axions, periodic scalar fields coupled to gauge fields through the instanton density, have a rich variety of higher-form global symmetries. These include a two-form global symmetry, which measures the charge of axion strings. As we review, these symmetries typically combine into a higher-group, a kind of non-abelian structure where symmetries that act on operators of different dimensions, such as points, lines, and strings, are mixed. We use this structure to derive model independent constraints on renormalization group flows that realize theories of axions at long distances. These give universal inequalities on the energy scales where various infrared symmetries emerge. For example, we show that in any UV completion of axion-Yang-Mills, the energy scale at which axion strings can decay is always larger than the mass scale of charged particles.

Non-Abelian Thouless pumping in a photonic lattice

Non-Abelian gauge fields emerge naturally in the description of adiabatically evolving quantum systems having degenerate levels. Here we show that they also play a role in Thouless pumping in the presence of degenerate bands. To this end we consider a photonic Lieb lattice having two degenerate nondispersive modes and show that, when the lattice parameters are slowly modulated, the propagation of the photons bears the fingerprints of the underlying non-Abelian gauge structure. The nondispersive character of the bands enables a high degree of control on photon propagation. Our work paves the way to the generation and detection of non-Abelian gauge fields in photonic and optical lattices.

Swampland cobordism conjecture and non-Abelian duality groups

We study the cobordism conjecture of McNamara and Vafa which asserts that the bordism group of quantum gravity is trivial. In the context of type IIB string theory compactified on a circle, this predicts the presence of D7-branes. On the other hand, the non-Abelian structure of the IIB duality group $SL(2,\mathbb{Z})$ implies the existence of additional $[p,q]$ 7-branes. We find that this additional information is instead captured by the space of closed paths on the moduli space of elliptic curves parameterizing distinct values of the type IIB axio-dilaton. This description allows to recover the full structure of non-Abelian braid statistics for 7-branes. Combining the cobordism conjecture with an earlier Swampland conjecture by Ooguri and Vafa, we argue that only certain congruence subgroups $\mathrm{\ensuremath{\Gamma}}\ensuremath{\subset}SL(2,\mathbb{Z})$ specifying genus zero modular curves can appear in 8D F-theory vacua. This leads to a successful prediction for the allowed Mordell--Weil torsion groups for 8D F-theory vacua.

Higher-rank tensor field theory of non-abelian fracton and embeddon

We formulate a new class of tensor gauge field theories in any dimension that is a hybrid class between symmetric higher-rank tensor gauge theory (i.e., higher-spin gauge theory) and anti-symmetric tensor topological field theory. Our theory describes a mixed unitary phase interplaying between gapless and gapped topological order phases (which can live with or without Euclidean, Poincaré, or anisotropic symmetry, at least in ultraviolet high or intermediate energy field theory, but not yet to a lattice cutoff scale). The “gauge structure” can be compact, continuous, abelian or non-abelian. Our theory sits outside the paradigm of Maxwell electromagnetic theory in 1865 and Yang–Mills isospin/color theory in 1954. We discuss its local gauge transformation in terms of the ungauged vector-like or tensor-like higher-moment global symmetry. The non-abelian gauge structure is caused by gauging the non-commutative symmetries: a higher-moment symmetry and a charge conjugation (particle–hole) symmetry. Vector global symmetries along time direction may exhibit time crystals. We explore the relation of these long-range entangled matters to a non-abelian generalization of Fracton order in condensed matter, a field theory formulation of foliation, the spacetime embedding and Embeddon that we newly introduce, and possible fundamental physics applications to dark matter or dark energy.

Non-simply-connected symmetries in 6D SCFTs

Six-dimensional mathcal{N} = (1, 0) superconformal field theories can be engineered geometrically via F-theory on elliptically-fibered Calabi-Yau 3-folds. We include torsional sections in the geometry, which lead to a finite Mordell-Weil group. This allows us to identify the full non-Abelian group structure rather than just the algebra. The presence of torsion also modifies the center of the symmetry groups and the matter representations that can appear. This in turn affects the tensor branch of these theories. We analyze this change for a large class of superconformal theories with torsion and explicitly construct their tensor branches. Finally, we elaborate on the connection to the dual heterotic and M-theory description, in which our configurations are interpreted as generalizations of discrete holonomy instantons.

Natural supersymmetric Twin Higgs

A new class of supersymmetric Twin Higgs (TH) models where new gauge symmetry is responsible for the TH mechanism is reviewed. In this class of models the Higgs mass is naturally in agreement with the LHC measurement while the electroweak symmetry breaking is realised without excessive tuning despite of strong lower bounds on masses of supersymmetric particles set by the LHC. Assuming particular non-abelian structure of the new gauge symmetry the model remains perturbative up to the energy scale of gravity, in contrast to all previously proposed UV completions of the TH model.

Infinite-Dimensional Carnot Groups and Gâteaux Differentiability

This paper contributes to the generalization of Rademacher’s differentiability result for Lipschitz functions when the domain is infinite dimensional and has nonabelian group structure. We introduce an infinite-dimensional analogue of Carnot groups that are metric groups equipped with dilations (which we call metric scalable groups) admitting a dense increasing sequence of finite-dimensional Carnot subgroups. For such groups, we show that every Lipschitz function has a point of Gâteaux differentiability. As a step in the proof, we show that a certain $$\sigma $$ -ideal of sets that are null with respect to this sequence of subgroups cannot contain open sets. We also give a geometric criterion for when such Carnot subgroups exist in metric scalable groups and provide examples of such groups. The proof of the main theorem follows the work of Aronszajn (Stud Math 57(2):147–190, 1976) and Pansu (Ann Math 129(1):1–60, 1989).

Quaternionic Formalism for Non-Abelian Gauge Theory of Dyons and Gravito-Dyons

Starting with the Quaternion formulation of SU (2 )× U (1)gauge theory of dyons and gravitodyons, it is shown that the formulation characterizes the abelian and non-Abelian gauge structure of dyons and gravito-dyons in terms of purely real and imaginary units of quaternion.

Quaternionic Formalism for Non-Abelian Gauge Theory of Dyons and Gravito-Dyons

Starting with the Quaternion formulation of SU (2 )× U (1)gauge theory of dyons and gravitodyons, it is shown that the formulation characterizes the abelian and non-Abelian gauge structure of dyons and gravito-dyons in terms of purely real and imaginary units of quaternion.

Authenticated group key agreement protocol based on twist conjugacy problem in near-rings

Nowadays some promising authenticated group key agreement protocols are constructed on braid groups, dynamic groups, pairings and bilinear pairings. Hence the non-abelian structure has attracted cryptographers to construct public-key cryptographic protocols. In this article, we propose a new authenticated group key agreement protocol which works in non-abelian near-rings. We have proved that our protocol meets the security attributes under the assumption that the twist conjugacy search problem (TCSP) is hard in near-ring.

Degenerate eigensubspace in a triangle-level system and its geometric quantum control

The non-Abelian geometric phases appear only in a degenerate subspace and the most familiar model with such a subspace is the $N$-pod system. Here we propose an alternative system to realize a non-Abelian gauge structure. We demonstrate that a three-level system with a triangular form can have two degenerate eigenstates which can induce non-Abelian geometric phases, and notably they are the lowest eigenstates of the system. As an application of the degenerate subspace, we propose an experimentally feasible scheme to realize a universal set of quantum gates based on the adiabatic non-Abelian geometric phases. To shorten the evolution time constrained by the adiabatic condition, the shortcut to adiabaticity is adopted to speed up the adiabatic geometric quantum gates. The combination of the intrinsic geometric characteristic and shortcut to adiabaticity makes the quantum operations fast and robust against certain control errors.

Deformed phase spaces with group valued momenta

We introduce a general framework for describing deformed phase spaces with group valued momenta. Using techniques from the theory of Poisson-Lie groups and Lie bi-algebras we develop tools for constructing Poisson structures on the deformed phase space starting from the minimal input of the algebraic structure of the generators of the momentum Lie group. The tools developed are used to derive Poisson structures on examples of group momentum space much studied in the literature such as the $n$-dimensional generalization of the $\kappa$-deformed momentum space and the $SL(2, \mathbb{R})$ momentum space in three space-time dimensions. We discuss classical momentum observables associated to multi-particle systems and argue that these combine according the usual four-vector addition despite the non-abelian group structure of momentum space.

Multiple fibrations in Calabi-Yau geometry and string dualities

In this work we explore the physics associated to Calabi-Yau (CY) n-folds that can be described as a fibration in more than one way. Beginning with F-theory vacua in various dimensions, we consider limits/dualities with M-theory, type IIA, and heterotic string theories. Our results include many M-/F-theory correspondences in which distinct F-theory vacua - associated to different elliptic fibrations of the same CY n-fold - give rise to the same M-theory limit in one dimension lower. Examples include 5-dimensional correspondences between 6-dimensional theories with Abelian, non-Abelian and superconformal structure, as well as examples of higher rank Mordell-Weil geometries. In addition, in the context of heterotic/F-theory duality, we investigate the role played by multiple K3- and elliptic fibrations in known and novel string dualities in 8-, 6- and 4-dimensional theories. Here we systematically summarize nested fibration structures and comment on the roles they play in T-duality, mirror symmetry, and 4-dimensional compactifications of F-theory with G-flux. This investigation of duality structures is made possible by geometric tools developed in a companion paper [1].

Cosmic ray air showers from sphalerons

The discovery of the Higgs boson marks a key ingredient to establish the electroweak structure of the Standard Model. Its non-abelian gauge structure gives rise to, yet unobserved, non-perturbative baryon and lepton number violating processes. We propose to use cosmic ray air showers, as measured at the Pierre Auger Observatory, to set a limit on the hadronic production cross section of sphalerons. We identify several observables to discriminate between sphaleron and QCD induced air showers.

Electric–magnetic dualities in non-abelian and non-commutative gauge theories

Electric–magnetic dualities are equivalence between strong and weak coupling constants. A standard example is the exchange of electric and magnetic fields in an abelian gauge theory. We show three methods to perform electric–magnetic dualities in the case of the non-commutative U(1) gauge theory. The first method is to use covariant field strengths to be the electric and magnetic fields. We find an invariant form of an equation of motion after performing the electric–magnetic duality. The second method is to use the Seiberg–Witten map to rewrite the non-commutative U(1) gauge theory in terms of abelian field strength. The third method is to use the large Neveu Schwarz–Neveu Schwarz (NS–NS) background limit (non-commutativity parameter only has one degree of freedom) to consider the non-commutative U(1) gauge theory or D3-brane. In this limit, we introduce or dualize a new one-form gauge potential to get a D3-brane in a large Ramond–Ramond (R–R) background via field redefinition. We also use perturbation to study the equivalence between two D3-brane theories. Comparison of these methods in the non-commutative U(1) gauge theory gives different physical implications. The comparison reflects the differences between the non-abelian and non-commutative gauge theories in the electric–magnetic dualities. For a complete study, we also extend our studies to the simplest abelian and non-abelian p-form gauge theories, and a non-commutative theory with the non-abelian structure.