Description
A detailed numerical study of a recent proposal for exotic
states of the D3-probe D5 brane system with charge density
and an external magnetic field is presented. The state has a
large number of coincident D5 branes blowing up to a D7
brane in the presence of the worldvolume electric and
magnetic fields which are necessary to construct the
holographic state. Numerical solutions have shown that these
states can compete with the the previously known chiral
symmetry breaking and maximally symmetric phases of the
D3-D5 system. Moreover, at integer filling fractions, they
are incompressible with integer quantized Hall
conductivities. In the dual superconformal defect field
theory, these solutions correspond to states which break the
chiral and global flavor symmetries spontaneously. The
region of the temperature-density plane where the D7 brane
has lower energy than the other known D5 brane solutions is
identified. A hypothesis for the structure of states with
filling fraction and Hall conductivity greater than one is
made and tested by numerical computation. A parallel with
the quantum Hall ferromagnetism or magnetic catalysis
phenomenon which is observed in graphene is drawn. As well
as demonstrating that the phenomenon can exist in a strongly
coupled system, this work makes a number of predictions of
symmetry breaking patterns and phase transitions for such
systems.