Thermal monopole condensation and confinement in finite temperature Yang-Mills theories

Abstract

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 condensation of such objects happening right at the deconfining transition. We also address the question of the thermal monopole mass, showing that different definitions give consistent results only around the transition, where the monopole mass goes down and becomes of the order of the critical temperature itself

StaticQ¯Qpotentials and the magnetic component of QCD plasma nearTc

“…This problem has recently been partially addressed in [39] where a relatively short life time is found in the classical treatment. On one hand from hydrodynamic modeling we know the near T c plasma has very small shear viscosity which indicates short mean free path and frequent scattering, while on the other hand for the magnetic currents to last long and hold the flux tube they better do not scatter too often: such a dilemma might be resolved if the thermal monopoles become really coherent over large distance at T close to T c and the lattice study supports such coherence [40]. These questions will be studied further elsewhere.…”

“…This indicates that near T c the monopoles should be very light, and furthermore their interactions should make it beneficial in energy to have a large number of monopole-antimonopole pairs. The monopoles are so dense and light that they become the dominant component in the near-T c plasma and presumably become quantum coherent, and eventually reach the condensation point at T c (see most recent lattice results in [40] showing evidences for such a scenario). It has been suggested that these thermal monopoles near T c seem to form a densely packed liquid [22] [25].…”

2d affine XY-spin model/4d gauge theory duality and deconfinement

“…This map is worked out in section 3, where the nature and role of the perturbative or non-perturbative objects driving the deconfinement transition is made quite explicit. We note that there have been earlier proposals and discussions of the role of various topological objects in the deconfinement transition, in the continuum and on the lattice, and that some bear resemblance to our discussion (see, for example, [14][15][16][17][18][19][20][21] and references therein). However, the study here stands out by being both analytic and under complete theoretical control.…”

“…Thus, including the W -bosons, in addition to the bions, we arrive at the following partition function (note that, as in (3.5), we absorb the factor of 2 from the bion charge in 21 A quick way to obtain this formula is to recall that unit electric charges appear as unit winding number vortices of the dual photon field in (2.1); then (3.9) is just the interaction energy of two vortices of unit winding. Equally quickly, since the interaction energy of two static W bosons in R 1,2 is g 2 2πL qaq b ln r ab and the W 's propagate in a (Euclidean) time interval 1 T , the corresponding action is precisely (3.9).…”

Study of the thermal Abelian monopoles with proper gauge fixing

“…There are a lot of definitions of the monopole mass (see [22]). In this paper we are going to apply the definition which is based on the formalism of functional integration.…”