Abstract
QCD monopoles are magnetically charged quasiparticles whose Bose-Einstein condensation (BEC) at $T<T_c$ creates electric confinement and flux tubes. The "magnetic scenario" of QCD proposes that scattering on the non-condensed component of the monopole ensemble at $T>T_c$ plays an important role in explaining the properties of strongly coupled quark-gluon plasma (sQGP) near the deconfinement temperature. In this paper, we study the phenomenon of chiral symmetry breaking and its relation to magnetic monopoles. Specifically, we study the eigenvalue spectrum of the Dirac operator in the basis of fermionic zero modes in an SU(2) monopole background. We find that as the temperature approaches the deconfinement temperature $T_c$ from above, the eigenvalue spectrum has a finite density at $\omega = 0$, indicating the presence of a chiral condensate. In addition, we find the critical scaling of the eigenvalue gap to be consistent with that of the correlation length in the 3d Ising model and the BEC transition of monopoles on the lattice.
Highlights
The possible existence of magnetic monopoles in electrodynamics fascinated leading physicists in the 19th century
We address how chiral symmetry breaking and the generation of the nonzero quark condensate at T < Tc can be explained in terms of this monopole model
Previous studies have shown that the deconfining phase transition of the Georgi-Glashow model falls in the Ising universality class [42,43]; our result is another confirmation of this property of the model
Summary
The possible existence of magnetic monopoles in electrodynamics fascinated leading physicists in the 19th century. With the advent of non-Abelian gauge theories, classical solitons with magnetic charge were found by ’t Hooft [2] and Polyakov [3] in the Georgi-Glashow model Such monopoles play important role in all other theories with an adjoint scalar field, notably in theories with extended supersymmetry N 1⁄4 2; 4. While the central role of monopoles in the confinementdeconfinement transition was recognized long ago, their relation to another important nonperturbative aspect of QCD-like theories, chiral symmetry breaking, has attracted much less attention It has been found on the lattice that, by decomposing the gauge fields into Abelian-monopole, Abelian-plain, and non-Abelian components, the removal of the monopoles does lead to removal of the quark condensate [30,31]. First we will remind the reader of the result found by Jackiw and Rebbi [35] for the fermionic zero modes, and go on to compute the matrix element between two monopoles in the basis of zero modes
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