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We study monopoles and corresponding t Hooft tensor in a generic gauge theory. This issue is relevant to the understanding of color confinement.
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We study monopoles and corresponding t Hooft tensor in QCD with a generic compact gauge group. This issue is relevant to the understanding of color confinement in terms of dual symmetry.
We discuss the lattice formulation of the t Hooft surface, that is, the two-dimensional surface operator of a dual variable. The t Hooft surface describes the world sheets of topological vortices. We derive the formulas to calculate the expectation value of the t Hooft surface in the multiple-charge lattice Abelian Higgs model and in the lattice non-Abelian Higgs model. As the first demonstration of the formula, we compute the intervortex potential in the charge-2 lattice Abelian Higgs model.
The dependence of the energies of axially symmetric monopoles of magnetic charges 2 and 3, on the Higgs self-interaction coupling constant, is studied numerically. Comparing the energy per unit topological charge of the charge-2 monopole with the energy of the spherically symmetric charge-1 monopole, we confirm that there is only a repulsive phase in the interaction energy between like monopoles
The number and the location of monopoles in Lattice configurations depend on the choice of the gauge, in contrast to the obvious requirement that monopoles, as physical objects, have a gauge-invariant status. It is proved, starting from non-abelian Bianchi identities, that monopoles are indeed gauge-invariant: the technique used to detect them has instead an efficiency which depends on the choice of the abelian projection, in a known and well understood way.
We analyze the vacuum structure of SU(2) lattice gauge theories in D=2,3,4, concentrating on the stability of t Hooft loops. High precision calculations have been performed in D=3; similar results hold also for D=4 and D=2. We discuss the impact of our findings on the continuum limit of Yang-Mills theories.
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