Abstract
Monopole-like objects have been identified in multiple lattice studies, and there is now a significant amount of literature on their importance in phenomenology. Some analytic indications of their role, however, are still missing. The 't Hooft-Polyakov monopoles, originally derived in the Georgi-Glashow model, are an important dynamical ingredient in theories with extended supersymmetry ${\cal N} = 2,\,4$, and help explain the issues related with electric-magnetic duality. There is no such solution in QCD-like theories without scalar fields. However, all of these theories have instantons and their finite-$T$ constituents known as instanton-dyons (or instanton-monopoles). The latter leads to semiclassical partition functions, which for ${\cal N} = 2,\,4$ theories were shown to be identical ("Poisson dual") to the partition function for monopoles. We show how, in a pure gauge theory, the semiclassical instanton-based partition function can also be Poisson-transformed into a partition function, interpreted as the one of moving and rotating monopoles.
Highlights
The possible existence of magnetic monopoles in electrodynamics fascinated leading physicists in the 19th century
With the development of quantum mechanics, Dirac [1] related the existence of monopoles with the electric charge quantization
Classical solitons with magnetic charge were found by ’t Hooft [2] and Polyakov [3] in the Georgi-Glashow model. Such monopoles exist and play an important role in other theories with an adjoint scalar field, notably in theories with extended supersymmetry N 1⁄4 2, 4. Their presence and properties have significantly advanced our understanding of the electric-magnetic duality and its relation to the renormalization group (RG) flow
Summary
The possible existence of magnetic monopoles in electrodynamics fascinated leading physicists in the 19th century. Classical solitons with magnetic charge were found by ’t Hooft [2] and Polyakov [3] in the Georgi-Glashow model Such monopoles exist and play an important role in other theories with an adjoint scalar field, notably in theories with extended supersymmetry N 1⁄4 2, 4. Their presence and properties have significantly advanced our understanding of the electric-magnetic duality and its relation to the renormalization group (RG) flow. The construction of the instanton-dyons starts from the same ’t Hooft-Polyakov monopole, but with the fourth component of the gauge field A4 acting as the scalar adjoint “Higgs” field These objects are pseudo-particles and not particles, existing only in the Euclidean formulation of the theory for which A4 is real. We Poisson-transform it into another form, the one we argue is counting occupations of the excited states of moving/ rotating monopoles
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