Holographic study of rho meson mass in an external magnetic field: paving the road towards a magnetically induced superconducting QCD vacuum?

Abstract: We study the rho meson mass in a uniform background magnetic field eB at zero temperature, in search of indications for the magnetically induced rho meson condensation, as predicted recently by Chernodub. The holographic model used is the Sakai-Sugimoto model with two flavours and a non-zero constituent quark mass. We fix the free holographic parameters by matching them to the phenomenological value for the constituent quark mass and the experimental values for the pion decay constant and the rho meson mass, this in absence of a magnetic field. In a first approximation, the Landau levels are recovered, indeed indicating an instability of the QCD vacuum at a critical magnetic field, eB_c ~ m_\rho^2, to a phase where rho mesons are condensed. We improve on this result by also taking into account the holographic analogue of chiral magnetic catalysis, numerically solving the mass eigenvalue equation for the rho meson, which depends on eB both explicitly and implicitly through the changed embedding of the flavour probe branes. This turns out to raise eB_c with a few percents. As a byproduct of our analysis we find that the separation between the chiral symmetry restoration temperature T_\chi(eB) and the deconfinement temperature T_c is 3.2 percent at eB = 30 m_\pi^2 ~ 0.57 GeV^2.