Embedded monopoles in quark eigenmodes in SU(2) Yang-Mills Theory

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 density of the Dirac eigenmodes. We observe, that the embedded monopoles corresponding to low-lying Dirac eigenvalues are dense in the chirally invariant (high temperature) phase and dilute in the chirally broken (low temperature) phase. We find that the scaling of the scalar and axial monopole densities towards the continuum limit is similar to the scaling of the string-like objects while the chirally invariant monopoles scale as membranes. The excess of gluon energy at monopole positions reveals that the embedded QCD monopole possesses a gluonic core, which is, however, empty at the very center of the monopole.Comment: 29 pages, 27 figures, RevTeX 4.0; revised to match the published version (clarifying remarks, references and acknowledgments are added

Magnetic Monopoles

This monograph addresses the field theoretical aspects of magnetic monopoles. Written for graduate students as well as researchers, the author demonstrates the interplay between mathematics and physics. He delves into details as necessary and develops many techniques that find applications in modern theoretical physics. This introduction to the basic ideas used for the description and construction of monopoles is also the first coherent presentation of the concept of magnetic monopoles. It arises in many different contexts in modern theoretical physics, from classical mechanics and electrodynamics to multidimensional branes. The book summarizes the present status of the theory and gives an extensive but carefully selected bibliography on the subject. The first part deals with the Dirac monopole, followed in part two by the monopole in non-abelian gauge theories. The third part is devoted to monopoles in supersymmetric Yang-Mills theories

Chains of Interacting Solitons

We present an overview of multisoliton chains arising in various non-integrable field theories and discuss different mechanisms which may lead to the occurrence of such axially-symmetric classical solutions. We explain the pattern of interactions between different solitons, in particular Q-balls, Skyrmions, and monopoles, and show how chains of interacting non-BPS solitons may form in a dynamic equilibrium between repulsive and attractive forces

Topological and non-topological solitons in scalar field theories

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