We explore the effect of magnetic field on chiral condensation in QCD via a
simple bottom up holographic model which inputs QCD dynamics through the
running of the anomalous dimension of the quark bilinear. Bottom up holography
is a form of effective field theory and we use it to explore the dependence on
the coefficients of the two lowest order terms linking the magnetic field and
the quark condensate. In the massless theory, we identify a region of parameter
space where magnetic catalysis occurs at zero temperature but inverse magnetic
catalysis at temperatures of order the thermal phase transition. The model
shows similar non-monotonic behaviour in the condensate with B at intermediate
T as the lattice data. This behaviour is due to the separation of the meson
melting and chiral transitions in the holographic framework. The introduction
of quark mass raises the scale of B where inverse catalysis takes over from
catalysis until the inverse catalysis lies outside the regime of validity of
the effective description leaving just catalysis.Comment: 9 pages, 8 figure
