Monopole solutions in SU(2) Yang-Mills theory which includes spinor fields described by the nonlinear Dirac equation are obtained. It is demonstrated that the energy spectrum of such a system possesses a global minimum whose appearance is brought about solely by the nonlinear spinor fields. It is shown that the monopole solution obtained differs in principle from the 't~Hooft-Polyakov monopole in that it is topologically trivial.
Within SU(2) Yang-Mills theory with a source of the non-Abelian gauge field in the form of a classical spinor field, we study the dependence of the mass gap on the coupling constant between the gauge and nonlinear spinor fields. It is shown that the total dimensionless energy of the monopole interacting with the nonlinear spinor fields depends only on the dimensionless coupling constant.
We study the properties of the mass gap for monopole solutions in SU(2) Yang-Mills theory with a source of the non-Abelian gauge field in the form of a spinor field described by the nonlinear Dirac equation. Different types of nonlinearities parameterized by the parameter $λ$ are under consideration. It is shown that for the range of values of this parameter studied in the present paper the value of the mass gap depends monotonically on this parameter, and the position of the mass gap does not practically depend on $λ$.
Yang-Mills theory is studied in a variant of 't Hooft's maximal Abelian gauge. In this gauge magnetic monopoles arise in the Abelian magnetic field. We show, however, that the full (non-Abelian) magnetic field does not possess any monopoles, but rather strings of magnetic fluxes. We argue that these strings are the relevant infrared degrees of freedom. The properties of the magnetic strings which arise from a dilute instanton gas are investigated for the gauge group SU(2).
We study the vacuum structure and dyon spectrum of N=2 supersymmetric gauge theory in four dimensions, with gauge group SU(2). The theory turns out to have remarkably rich and physical properties which can nonetheless be described precisely; exact formulas can be obtained, for instance, for electron and dyon masses and the metric on the moduli space of vacua. The description involves a version of Olive-Montonen electric-magnetic duality. The ``strongly coupled'' vacuum turns out to be a weakly coupled theory of monopoles, and with a suitable perturbation confinement is described by monopole co…
We present a systematic procedure to compute complete, analytic form factors of gauge-invariant operators at loop level in pure Yang-Mills. We consider applications to operators of the form $\mathrm{Tr}\, F^n$ where $F$ is the gluon field strength. Our approach is based on an extension to form factors of the dimensional reconstruction technique, in conjunction with the six-dimensional spinor-helicity formalism and generalised unitarity. For form factors this technique requires the introduction of additional scalar operators, for which we provide a systematic prescription. We also discuss a gen…
Scaling behavior in the moduli space of monopole and dyon solutions in the Einstein-Yang-Mills theory in the asymptotically anti-de Sitter space is derived. The mass of monopoles and dyons scales with respect to their magnetic and electric charges, independent of the values of the cosmological constant and gauge coupling constant. The stable monopole and dyon solutions are approximated by solutions in the fixed anti-de Sitter spacetime. Unstable solutions can be viewed as the Bartnik-McKinnon solutions dressed with monopole and dyon solutions in the fixed anti-de Sitter space.
A gauge transformation provided by the three eigenfunctions of $\B^a(x) \cdot \B^b(x)$ (where $\B^a(x)$, with a=1,2,3, are the non-Abelian magnetic fields) exposes the topological configurations of the Yang-Mills fields. In particular, it gives Dirac monopoles interacting with `photons' and massless charged vector bosons. A magnetic dipole field at each monopole corresponds to infinitesimal translation of the monopole, and provides the functional measure a la collective coordinates. The grand canonical partition function of the monopole plasma is exactly equivalent to a local field theory with…
We study the Yang-Mills-Higgs system within the framework of general relativity. In the static situation, using Bogomol'nyi type analysis, we derive a positive-definite energy functional which has a lower bound. Specializing to the gauge group $SU(2)$ and the t'Hooft-Polyakov ansatz for the gauge and Higgs fields, we seek static, spherically symmetric solutions to the coupled system of equations in both the isotropic and standard coordinate systems. In both cases, in the spontaneously broken symmetry situation, we find great simplications reducing the solutions of the coupled system to the sol…
We give an analytical solution representing circular magnetic monopole loops joining a pair of merons in the four-dimensional Euclidean SU(2) Yang-Mills theory. This is achieved by solving the differential equation for the adjoint color (magnetic monopole) field in the two--meron background field within the recently developed reformulation of the Yang-Mills theory. Our analytical solution corresponds to the numerical solution found by Montero and Negele on a lattice. This result strongly suggests that a meron pair is the most relevant quark confiner in the original Yang-Mills theory, as Callan…
We investigate the connection between Color Confinement and thermal Abelian monopoles populating the deconfined phase of SU(2) Yang-Mills theory, by studying how the statistical properties of the monopole ensemble change as the confinement/deconfinement temperature is approached from above. In particular we study the distribution of monopole currents with multiple wrappings in the Euclidean time direction, corresponding to two or more particle permutations, and show that multiple wrappings increase as the deconfinement temperature is approached from above, in a way compatible with a condensati…
We study the embedded QCD monopoles (``quark monopoles'') using low-lying eigenmodes of the overlap Dirac operator in zero- and finite-temperature SU(2) Yang-Mills theory on the lattice. These monopoles correspond to the gauge-invariant hedgehogs in the quark-antiquark condensates. The monopoles were suggested to be agents of the chiral symmetry restoration since their cores should suppress the chiral condensate. We study numerically the scalar, axial and chirally invariant definitions of the embedded monopoles and show that the monopole densities are in fact globally anti-correlated with the …
We present recent results on quark confinement: in SU(3) Yang-Mills theory, confinement of fundamental quarks is obtained due to the dual Meissner effect originated from non-Abelian magnetic monopoles defined in a gauge-invariant way, which is distinct from the well-known Abelian projection scenario. This is achieved by using a non-Abelian Stokes theorem for the Wilson loop operator and a new reformulation of the Yang-Mills theory.
We review some recent developments on BPS string solutions and monopole confinement in the Higgs or (color) superconducting phase of deformed N=2 and N=4 super Yang-Mills theories. In particular, the monopole magnetic fluxes are shown to be always integer linear combinations of string fluxes. Moreover, a bound for the threshold length of the string breaking is obtained. When the gauge group SU(N) is broken to Z_N, the BPS string tension satisfies the Casimir scaling law. Furthermore in the SU(3) case the string solutions are such that they allow the formation of a confining system with three m…
We discuss a non-minimal Einstein-Yang-Mills-Higgs model with uniaxial anisotropy in the group space associated with the Higgs field. We apply this theory to the problem of propagation of color and color-acoustic waves in the gravitational background related to the non-minimal regular Wu-Yang monopole.
We use the SU(2) 't Hooft-Polyakov monopole configuration, and its BPS version, to test the integral equations of the Yang-Mills theory. Those integral equations involve two (complex) parameters which do not appear in the differential Yang-Mills equations, and if they are considered to be arbitrary it then implies that non-abelian gauge theories (but not abelian ones) possess an infinity of integral equations. For static monopole configurations only one of those parameters is relevant. We expand the integral Yang-Mills equation in a power series of that parameter and show that the 't Hooft-Pol…
Dark sectors with Abelian gauge symmetries can interact with ordinary matter via kinetic mixing. In such scenarios, magnetic monopoles of a broken dark $U(1)$ will appear in our sector as confined milli-magnetically charged objects under ordinary electromagnetism. Halo ellipticity constraints are shown to significantly bound the strength of dark magnetic Coulomb monopole interactions. The bound monopole ground state, which in vacuum is stable and has no magnetic charge or moment, is shown to become quantum mechanically unstable in the presence of an external, ordinary magnetic field. If these …
We study the Z_N flux tubes and monopole confinement in deformed N=2* super Yang-Mills theories. In order to do that we consider an N=4 super Yang-Mills theory with an arbitrary gauge group G and add some N=2, N=1 and N=0 deformation terms. We analyze some possible vacuum solutions and phases of the theory, depending on the deformation terms which are added. In the Coulomb phase for the N=2* theory, G is broken to U(1)^r and the theory has monopole solutions. Then, by adding some deformation terms, the theory passes to the Higgs or color superconducting phase, in which G is broken to its cente…
We consider bound states of fermions with an anomalous magnetic moments(neutrinos,neutrons) in radial electric and magnetic field of monopole.In case of radial magnetic field the interaction $\vecΣ\vec{H}$ violates P-parity and for this reason we must use the method of (hep-ph/9901248) where both components of spinor considererd as a linear combination of spheric spinors with different P-parity. Also we apply pseudoscalar-like interaction (2) obtained in \cite{DF} to monopole case and add it in Dirac equation.We obtain the system of differential equations for radial functions which define ener…
By extending the Cho decomposition method to G(2) gauge group, monopoles of this group are studied. Since SU(2) and SU(3) are subgroups of G(2), discussions are done mostly based on these subgroups of G(2). A direct relation between root vectors of G(2) and the associated magnetic charges is presented by group theoretical issues. In addition, G(2) monopoles are obtained by an Abelian gauge fixing method, and it is shown that the results agree with the ones we obtain by the Cho decomposition method.
We show that the QCD vacuum (without dynamical quarks) is a dual superconductor at least in the low-energy region in the sense that monopole condensation does really occur. In fact, we derive the dual Ginzburg-Landau theory (i.e., dual Abelian Higgs model) directly from the SU(2) Yang-Mills theory by adopting the maximal Abelian gauge. The dual superconductor can be on the border between type II and type I, excluding the London limit. The masses of the dual Abelian gauge field is expressed by the Yang-Mills gauge coupling constant and the mass of the off-diagonal gluon of the original Yang-Mil…
Condensation of the Abelian monopoles and the center vortices leads to confinement of color in low temperature phase of Yang-Mills theory. We stress that these topological magnetic degrees of freedom are also very important in the deconfinement regime: at the point of the deconfinement phase transition both the monopoles and the vortices are released into the thermal vacuum contributing, in particular, to the equation of state and, definitely, to transport properties of the hot gluonic medium. Thus, we argue that a novel, magnetic component plays a crucial role. On the other hand, it was demon…
We discuss the role of magnetic degrees of freedom in Yang-Mills plasma at temperatures above and of order of the critical temperature Tc. While at zero temperature the magnetic degrees of freedom are condensed and electric degrees of freedom are confined, at the point of the phase transition both magnetic and electric degrees of freedom are released into the thermal vacuum. This phenomenon might explain the observed unusual properties of the plasma.
We show how vortices can appear in the low energy limit of a pure SU(2) Yang-Mills theory as topological solitons. Motivated by Abelian dominance, we suppose that in the infrared regime of the SU(2) Yang-Mills theory, the field strength tensor can be obtained by multiplying two parts: $ G_{μν} $ and $ \textbf{n} $ such that $ \textbf{G}_{μν}=G_{μν} \textbf{n} $. The first part, $ G_{μν} $, is a space-time tensor and the second part, $ \textbf{n} $, is an isotriplet unit vector field which gives the Abelian direction at each space-time point. This leads to a decomposition for the SU(2) Yang-Mil…
Confinement in non-Abelian gauge theories is commonly ascribed to percolation of magnetic monopoles, or strings in the vacuum. At the deconfinement phase transition the condensed magnetic degrees of freedom are released into gluon plasma as thermal magnetic monopoles. We point out that within the percolation picture lattice simulations can be used to estimate the monopole content of the gluon plasma. We show that right above the critical temperature the monopole density remains a constant function of temperature, as for a liquid, and then grows, like for a gas.
We investigate the properties of thermal abelian magnetic monopoles in the high temperature phase of Yang--Mills theories, following a recent proposal for their identification on lattice configurations. The study is done for SU(2) pure gauge theory, for temperatures going up to about 10 times the deconfining temperature and using the Maximal Abelian gauge to perform the abelian projection. We find that the monopole density has a well defined continuum limit. Its temperature dependence disagrees with a free particle gas prediction and is instead well described by a $T^3/(\log (T/Λ))^α$ behaviou…
Characterizing the vacuum of a thermalized SU(3) Yang-Mills theory in the dual Ginzburg-Landau description, the possibility of topologically nontrivial, classical monopole fields in the deconfining phase is explored. These fields are assumed to be Bogomoln'yi-Prasad-Sommerfield (BPS) saturated solutions along the compact, euclidean time dimension. A corresponding, gauge invariant monopole interaction is constructed. The model passes first tests. In particular, a reasonable value for the critical temperature is obtained, and the partial persistence of nonperturbative features in the deconfining…
