We study the rho meson in a uniform magnetic field eB using a holographic
QCD-model, more specifically a D4/D8/Dbar8 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_rho^2 towards a phase where charged rho
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 rho meson condensation to eB = 1.1
m_rho^2 = 0.67 GeV^2. We briefly discuss the influence of pions, which turn out
to be irrelevant for the condensation in the approximation made.Comment: 26 pages, 10 .pdf figures, v2: version accepted for publication in
JHE
