non-Abelian Magnetic Monopoles Research Articles

Hidden symmetries, spin and charge of artificial magnetic monopoles

We discuss the non-Abelian artificial magnetic monopoles associated with n-level energy crossing in quantum systems. We found that hidden symmetries reveal themselves as observables such as spin, hypercharge, and other physical degrees of freedom. We illustrated our results on concrete examples of two and three energy-level crossings. Our findings can be helpful for modeling various phenomena in physical systems such as SU(N) topological insulators and spintronic devices based on topological insulators.

Critical Solutions of Scalarized Black Holes

We consider charged black holes with scalar hair obtained in a class of Einstein–Maxwell– scalar models, where the scalar field is coupled to the Maxwell invariant with a quartic coupling function. Besides the Reissner–Nordström black holes, these models allow for black holes with scalar hair. Scrutinizing the domain of existence of these hairy black holes, we observe a critical behavior. A limiting configuration is encountered at a critical value of the charge, where space time splits into two parts: an inner space time with a finite scalar field and an outer extremal Reissner–Nordström space time. Such a pattern was first observed in the context of gravitating non-Abelian magnetic monopoles and their hairy black holes.

Testing the new BPS method in some models of nonabelian magnetic monopole

The proposed method in [Phys. Lett. B768 351-358 (2017)], which can obtain BPS equations of some models of vortices, is used here to see whether it is still usable for some models of magnetic monopole. Other than the standard Yang-Mills-Higgs, here we report that the method is able to give us the BPS equations from two different magnetic monopole models.

Emergence of Non-Abelian Magnetic Monopoles in a Quantum Impurity Problem.

Recently, it was shown that molecules rotating in superfluid helium can be described in terms of the angulon quasiparticles [Phys. Rev. Lett. 118, 095301 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.095301]. Here, we demonstrate that in the experimentally realized regime the angulon can be seen as a point charge on a two-sphere interacting with a gauge field of a non-Abelian magnetic monopole. Unlike in several other settings, the gauge fields of the angulon problem emerge in the real coordinate space, as opposed to the momentum space or some effective parameter space. Furthermore, we find a topological transition associated with making the monopole Abelian, which takes place in the vicinity of the previously reported angulon instabilities. These results pave the way for studying topological phenomena in experiments on molecules trapped in superfluid helium nanodroplets, as well as on other realizations of orbital impurity problems.

Constructing the quantum Hall system on the Grassmannians Gr2(CN)

In this talk, we give the formulation of Quantum Hall Effects (QHEs) on the complex Grassmann manifolds Gr2(CN). We set up the Landau problem in Gr2(CN), solve it using group theoretical techniques and provide the energy spectrum and the eigenstates in terms of the SU(N) Wigner D-functions for charged particles on Gr2(CN) under the influence of abelian and non-abelian background magnetic monopoles or a combination of these thereof. For the simplest case of Gr2(C4) we provide explicit constructions of the single and many- particle wavefunctions by introducing the Plucker coordinates and show by calculating the two-point correlation function that the lowest Landau level (LLL) at filling factor v = 1 forms an incompressible fluid. Finally, we heuristically identify a relation between the U(1) Hall effect on Gr2(C4) and the Hall effect on the odd sphere S5, which is yet to be investigated in detail, by appealing to the already known analogous relations between the Hall effects on CP3 and CP7 and those on the spheres S4 and S8, respectively. The talk is given by S. Kürkçüoğlu at the Group 30 meeting at Ghent University, Ghent, Belgium in July 2014 and based on the article by F.Ballı, A.Behtash, S. Kürkçüoğlu, G.Ünal [1].

Generalized dyons and magnetic dipoles: The issue of angular momentum

It is known that a non-Abelian magnetic monopole cannot rotate globally (although it may possess a nonzero angular momentum density). At the same time, the total angular momentum of a magnetic dipole equals the electric charge. In this work we question the generality of these results by considering a number of generalizations of the Georgi-Glashow model. We study two different types of finite energy, regular configurations: solutions with net magnetic charge and monopole-antimonopole pairs with zero net magnetic charge. These configurations are endowed with an electric charge and carry also a nonvanishing angular momentum density. However, we argue that the qualitative results found in the Georgi-Glashow model are generic and thus a magnetic monopole cannot spin as long as the matter fields feature the usual ``monopole'' asymptotic behavior independently of the dynamics of the model. A study of the properties of the dyons and magnetic dipoles in some generalizations of the Georgi-Glashow model supplemented with higher order Skyrme-like terms in the gauge curvature and Higgs fields is given quantitatively.

On ’t Hooft–Polyakov Monopole, Julia–Zee Dyon, and Higgs Field, throughout the Generalized Bogomoln’yi Equations

In this paper, making use of the 't Hooft-Polyakov-Julia-Zee ansatz for the SU(2) Yang-Mills-Higgs gauge field theory, we present the straightforward generalization of the Bogomoln'yi equations and its several consequences. Particularly, this is shown that this idea is able to generate new types of non-abelian both dyons and magnetic monopoles and, moreover, that within the new model the scalar field can be described through the Coulomb potential, whereas, up to a constant, the non-abelian gauge field becomes the Wu-Yang monopole.

Quantum Hall effect on the GrassmanniansGr2(CN)

Quantum Hall effects on the complex Grassmann manifolds ${\mathbf{Gr}}_{2}({\mathbb{C}}^{N})$ are formulated. We set up the Landau problem in ${\mathbf{Gr}}_{2}({\mathbb{C}}^{N})$ and solve it using group theoretical techniques and provide the energy spectrum and the eigenstates in terms of the $SU(N)$ Wigner $\mathcal{D}$ functions for charged particles on ${\mathbf{Gr}}_{2}({\mathbb{C}}^{N})$ under the influence of Abelian and non-Abelian background magnetic monopoles or a combination of these. In particular, for the simplest case of ${\mathbf{Gr}}_{2}({\mathbb{C}}^{4})$, we explicitly write down the $U(1)$ background gauge field as well as the single- and many-particle eigenstates by introducing the Pl\"ucker coordinates and show by calculating the two-point correlation function that the lowest Landau level at filling factor $\ensuremath{\nu}=1$ forms an incompressible fluid. Our results are in agreement with the previous results in the literature for the quantum Hall effect on $\mathbb{C}{P}^{N}$ and generalize them to all ${\mathbf{Gr}}_{2}({\mathbb{C}}^{N})$ in a suitable manner. Finally, we heuristically identify a relation between the $U(1)$ Hall effect on ${\mathbf{Gr}}_{2}({\mathbb{C}}^{4})$ and the Hall effect on the odd sphere ${S}^{5}$, which is yet to be investigated in detail, by appealing to the already-known analogous relations between the Hall effects on $\mathbb{C}{P}^{3}$ and $\mathbb{C}{P}^{7}$ and those on the spheres ${S}^{4}$ and ${S}^{8}$, respectively.

Non-Abelian dual superconductivity inSU(3)Yang-Mills theory: Dual Meissner effect and type of the vacuum

We have proposed the non-Abelian dual superconductivity picture for quark confinement in the SU(3) Yang-Mills (YM) theory, and have given numerical evidences for the restricted-field dominance and the non-Abelian magnetic monopole dominance in the string tension by applying a new formulation of the YM theory on a lattice. To establish the non-Abelian dual superconductivity picture for quark confinement, we have observed the non-Abelian dual Meissner effect in the SU(3) Yang-Mills theory by measuring the chromoelectric flux created by the quark-antiquark source, and the non-Abelian magnetic monopole currents induced around the flux. We conclude that the dual superconductivity of the SU(3) Yang-Mills theory is strictly the type I and that this type of dual superconductivity is reproduced by the restricted field and the non-Abelian magnetic monopole part, in sharp contrast to the SU(2) case: the border of type I and type II.

Mixed states from anomalies

There are several instances where quantum anomalies of continuous and discrete classical symmetries play an important role in fundamental physics. Examples come from chiral anomalies in the Standard Model of fundamental interactions and gravitational anomalies in string theories. Their generic origin is the fact that classical symmetries may not preserve the domains of quantum operators like the Hamiltonian. In this work, we show by simple examples that anomalous symmetries can often be implemented at the expense of working with mixed states having nonzero entropies. In particular there is the result on color breaking by non-abelian magnetic monopoles. This anomaly can be rectified by using impure states. We also argue that non-abelian groups of twisted bundles are always anomalous for pure states sharpening an earlier argument of Sorkin and Balachandran [A. P. Balachandran, G. Marmo, B. S. Skagerstam, and A. Stern, Classical Topology and Quantum States (World Scientific, Singapore, 1991).]. This is the case of mapping class groups of geons [A. P. Balachandran, G. Marmo, B. S. Skagerstam, and A. Stern, Classical Topology and Quantum States (World Scientific, Singapore, 1991).] indicating that large diffeos are anomalous for pure states in the presence of geons. Nevertheless diffeo invariance may be restored by using impure states. This work concludes with examples of these ideas drawn from molecular physics. The above approach using impure states is entirely equivalent to restricting all states to the algebra of observables invariant under the anomalous symmetries. For anomalous gauge groups such as color, this would mean that we work with observables singlet under global gauge transformations. For color, this will mean that we work with color singlets, a reasonable constraint.

Non-Abelian dual superconductor picture for quark confinement

We give a theoretical framework for defining and extracting non-Abelian magnetic monopoles in a gauge-invariant way in SU(N) Yang-Mills theory to study quark confinement. Then we give numerical evidences that the non-Abelian magnetic monopole defined in this way gives a dominant contribution to confinement of fundamental quarks in SU(3) Yang-Mills theory, which is in sharp contrast to the SU(2) case in which Abelian magnetic monopoles play the dominant role for quark confinement.

Quantized non-Abelian monopoles onS3

A possible electric-magnetic duality suggests that the confinement of non-Abelian electric charges manifests itself as a perturbative quantum effect for the dual magnetic charges. Motivated by this possibility, we study vacuum fluctuations around a non-Abelian monopole-antimonopole pair treated as point objects with charges g={+-}n/2 (n=1,2,...), and placed on the antipodes of a three sphere of radius R. We explicitly find all the fluctuation modes by linearizing and solving the Yang-Mills equations about this background field on a three sphere. We recover, generalize, and extend earlier results, including those on the stability analysis of non-Abelian magnetic monopoles. We find that for g{>=}1 monopoles there is an unstable mode that tends to squeeze magnetic flux in the angular directions. We sum the vacuum energy contributions of the fluctuation modes for the g=1/2 case and find oscillatory dependence on the cutoff scale. Subject to certain assumptions, we find that the contribution of the fluctuation modes to the quantum zero-point energy grows as {approx}-R{sup -2/3} and hence decays more slowly than the classical -R{sup -1} Coulomb potential for large R. However, the growth of the zero-point energy does not agree with the linear growth expected if the monopoles are confined.

Nutty dyons

We argue that the Einstein–Yang–Mills–Higgs theory presents nontrivial solutions with a NUT charge. These solutions approach asymptotically the Taub–NUT spacetime and generalize the known dyon black hole configurations. The main properties of the solutions and the differences with respect to the asymptotically flat case are discussed. We find that a non-Abelian magnetic monopole placed in the field of gravitational dyon necessarily acquires an electric field, while the magnetic charge may take arbitrary values.

Non-Abelian color dielectric - towards the effective model of the low energy QCD

Lattice motivated triplet color scalar field theory is analyzed. We consider non-minimal as well as covariant derivative coupling with SU(2) gauge fields. Field configurations generated by external electric sources are presented. Moreover non-Abelian magnetic monopoles are found. Dependence on the spatial coordinates in the obtained solutions is identical as in the usual Abelian case. We show also that after a decomposition of the fields a modified Faddeev-Niemi action can be obtained. It contains explicit O(3) symmetry breaking term parameterized by the condensate of an isoscalar field. Due to that Goldstone bosons observed in the original Faddeev-Niemi model are removed.

Non-Abelian monopoles

We study topological as well as dynamical properties of BPS non-Abelian magnetic monopoles of Goddard–Nuyts–Olive–Weinberg type in G = SU ( N ) , USp ( 2 N ) and SO ( N ) gauge theories, spontaneously broken to non-Abelian subgroups H. We find that monopoles transform under the group dual to H in a tensor representation of rank determined by the corresponding element in π 1 ( H ) . When the system is embedded in a N = 2 supersymmetric theory with an appropriate set of flavors with appropriate bare masses, the BPS monopoles constructed semiclassically persist in the full quantum theory. This result supports the identification of “dual quarks” found at r-vacua of N = 2 theories with the non-Abelian magnetic monopoles. We present several consistency checks of our monopole spectra.

Non-Abelian monopoles and the vortices that confine them

Non-Abelian magnetic monopoles of Goddard–Nuyts–Olive–Weinberg type have recently been shown to appear as the dominant infrared degrees of freedom in a class of softly broken N=2 supersymmetric gauge theories in which the gauge group G is broken to various non-Abelian subgroups H by an adjoint Higgs VEV. When the low-energy gauge group H is further broken completely by, e.g., squark VEVs, the monopoles representing π 2( G/ H) are confined by the non-Abelian vortices arising from the breaking of H, discussed recently [ hep-th/0307278]. By considering the system with G= SU( N+1), H= SU(N)×U(1) Z N , as an example, we show that the total magnetic flux of the minimal monopole agrees precisely with the total magnetic flux flowing along the single minimal vortex. The possibility for such an analysis reflects the presence of free parameters in the theory—the bare quark mass m and the adjoint mass μ—such that for m⪢ μ the topologically nontrivial solutions of vortices and of unconfined monopoles exist at distinct energy scales.

Nonabelian superconductors: vortices and confinement in [formula omitted] SQCD

We study nonabelian vortices (flux tubes) in SU( N) gauge theories, which are responsible for the confinement of (nonabelian) magnetic monopoles. In particular a detailed analysis is given of N=2 SQCD with gauge group SU(3) deformed by a small adjoint chiral multiplet mass. Tuning the bare quark masses (which we take to be large) to a common value m, we consider a particular vacuum of this theory in which an SU(2) subgroup of the gauge group remains unbroken. We consider 5⩾ N f ⩾4 flavors so that the SU(2) sub-sector remains non asymptotically free: the vortices carrying nonabelian fluxes may be reliably studied in a semi-classical regime. We show that the vortices indeed acquire exact zero modes which generate global rotations of the flux in an SU(2) C+ F group. We study an effective world sheet theory of these orientational zero modes which reduces to an N=2 O(3) sigma model in 1+1 dimensions. Mirror symmetry then teaches us that the dual SU(2) group is not dynamically broken.

Almost conformal vacua and confinement

Dynamics of confining vacua which appear as deformed superconformal theory with a non-Abelian gauge symmetry, is studied by taking a concrete example of the sextet vacua of N=2 , SU(3) gauge theory with n f =4, with equal quark masses. We show that the low-energy “matter” degrees of freedom of this theory consist of four magnetic monopole doublets of the low-energy effective SU(2) gauge group, one dyon doublet, and one electric doublet. We find a mechanism of cancellation of the beta function, which naturally but nontrivially generalizes that of Argyres–Douglas. Study of our SCFT theory as a limit of six colliding N=1 vacua, suggests that the confinement in the present theory occurs in an essentially different manner from those vacua with dynamical abelianization, and involves strongly interacting non-Abelian magnetic monopoles.

Non-Abelian magnetic monopoles and dynamics of confinement

Magnetic monopoles having non-Abelian charges have been found recently to play a crucial role in the infrared in a class of supersymmetric gauge theories. We argue that these “dual quarks” can naturally be identified with the non-Abelian magnetic monopoles of the type first discussed by Goddard, Nuyts and Olive. Our argument is based on a few simple observations as regards to their charge structure, flavor quantum numbers, and some general properties of electromagnetic duality.

Electric-magnetic duality in supersymmetric non-Abelian gauge theories

We demonstrate electric-magnetic duality in N = 1 supersymmetric non-Abelian gauge theories in four dimensions by presenting two different gauge theories (different gauge groups and quark representations) leading to the same non-trivial long distance physics. The quarks and gluons of one theory can be interpreted as solitons (non-Abelian magnetic monopoles) of the elementary fields of the other theory. The weak coupling region of one theory is mapped to a strong coupling region of the other. When one of the theories is Higgsed by an expectation value of a squark, the other theory is confined. Massless glueballs, baryons and Abelian magnetic monopoles in the confining description are the weakly coupled elementary quarks (i.e. solitons of the confined quarks) in the dual Higgs description.