General structure of relativistic vector condensation

Abstract

We study relativistic massive vector condensation due to a non zero chemical potential associated to some of the global conserved charges of the theory. We show that the phase structure is very rich. More specifically there are three distinct phases depending on the value of one of the zero chemical potential vector self interaction terms. We also develop a formalism which enables us to investigate the vacuum structure and dispersion relations in the spontaneously broken phase of the theory. We show that in a certain limit of the couplings and for large chemical potential the theory is not stable. This limit, interestingly, corresponds to a gauge type limit often employed to economically describe the ordinary vector mesons self interactions in QCD. We finally indicate for which physical systems our analysis is relevant.

Rho meson condensation at finite isospin chemical potential in a holographic model for QCD

“…In the D8-brane configurations we discussed above, there are two independent U(Nf ) gauge fields living near the boundary of space-time; one gauge field (A L µ ) living at x 4 = 0 and another (A R µ ) living at x 4 = L. Thus, these theories have a U(Nf ) L × U(Nf ) R global symmetry. 7 Note that in this case the gauge fields near the boundary are only functions of 3 + 1 out of the 4 + 1 dimensions of the gauge theory, reflecting the fact that the global symmetry acts on fields which are localized in 3 + 1 dimensions.…”

Review of Vector Condensation at High Chemical Potential

“…All of the physical states (with and without a gap) are either vectors (2-component) or scalars with respect to the unbroken SO(2) group. The dispersion relations for the 3 gapless states can be found in [15]. At µ = m the dispersion relations are no longer linear in the momentum.…”

“…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 [22,16,15].…”

“…We set δ = 0 and the theory gains a new symmetry according to which we have always a total number of even vectors in any process [15]. The effect of a nonzero chemical potential associated to a given conserved charge -(say T 3 = τ 3 /2) -can be included by modifying the derivatives acting on the vector fields according to…”

“…If the chemical potential is sufficiently high one can show that the gaps (i.e. the energy at zero momentum) of these vectors become light [15,16,17] and eventually zero signaling an instability. If one applies our results to 2 color Quantum Chromo Dynamics (QCD) at non zero baryon chemical potential one predicts that the vectors made out of two quarks (in the 2 color theory the baryonic degrees of freedom are bosons) condense.…”