Holographic ρ mesons in an external magnetic field

We study the ρ meson in a uniform magnetic field eB using a holographic QCD-model, more specifically a D4/D8/D8̄ brane setup in the confinement phase at zero temperature with two quenched flavours. The parameters of the model are fixed by matching to corresponding dual field theory parameters at zero magnetic field. We show that the up- and down-flavour branes respond differently to the presence of the magnetic field in the dual QCD-like theory, as expected because of the different electromagnetic charge carried by up- and down-quark. We discuss how to recover the Landau levels, indicating an instability of the QCD vacuum at eB=m towards a phase where charged ρ mesons are condensed, as predicted by Chernodub using effective QCD-models. We improve on these existing effective QCD-model analyses by also taking into account the chiral magnetic catalysis effect, which tells us that the constituent quark masses rise with eB. This turns out to increase the value of the critical magnetic field for the onset of ρ meson condensation to eB\approx 1.1\;mρ2\approx 0.67\GeV2. We briefly discuss the influence of pions, which turn out to be irrelevant for the condensation in the approximation made. © 2013 SISSA, Trieste, Italy.