Electric-magnetic asymmetry of theA2condensate and the phases of Yang-Mills theory

Abstract

We study the finite-temperature behavior of the ${A}^{2}$ condensate in the Landau gauge of $SU(2)$ Yang-Mills theory on the lattice in a wide range of temperatures. The asymmetry between the electric (temporal) and magnetic (spatial) components of this unconventional dimension-2 condensate is a convenient ultraviolet-finite quantity which possesses, as we demonstrate, unexpected properties. The low-temperature behavior of the condensate asymmetry suggests that the mass of the lowest thermal excitation in the condensate is unexpectedly low, about 200 MeV, which is much smaller than the glueball mass. The asymmetry is peaking at the phase transition, becoming a monotonically decreasing function in the deconfinement phase. A symmetric point is reached in the deconfinement phase at a temperature approximately equal to twice the critical temperature. The behavior of the electric-magnetic asymmetry of the condensate separates the phase diagram of Yang-Mills theory into three regions. We suggest that these regions are associated with the condensed, liquid, and gaseous states of the confining gluonic objects, the Abelian monopoles.