Relativistic massive vector condensation

Abstract

At sufficiently high chemical potential massive relativistic spin one fields condense. This phenomenon leads to the spontaneous breaking of rotational invariance while linking it to the breaking of internal symmetries. We study the relevant features of the phase transition and the properties of the generated Goldstone excitations. The interplay between the internal symmetry of the vector fields and their Lorentz properties is studied. We predict that new phases set in when vectors condense in Quantum Chromodynamics like theories.

General structure of relativistic vector condensation

“…Expanding the potential around the vacuum we find 5 null curvatures [12]. However we have only three gapless states obtained diagonalizing the quadratic kinetic term and the potential term (see the dispersion relation section).…”

“…This phase has been partially analyzed in [12]. We have the following pattern of symmetry breaking SO(3) × U (1) → SO(2).…”

“…At µ = m the dispersion relations are no longer linear in the momentum. This is related to the fact that the specific part of the potential term has a partial conformal symmetry discussed first in [12]. Some states in the theory are curvatureless but the chemical potential term present in the derivative term prevents these states to be gapless.…”

“…There is a transfer of the conformal symmetry information from the potential term to the vanishing of the velocity of the gapless excitations related to the would be gapless states. This conversion is due to the linear time-derivative term induced by the presence of the chemical potential term [12,18].…”

“…The polar phase, the apolar phase and the enhanced symmetry one. The polar phase has been introduced in [12] along with the enhanced symmetry case. The polar and apolar phases are the relativistic generalization of the phases encountered in the condense matter [16] framework.…”