Abstract
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.
Highlights
The higher level which is separated from the ones that are already occupied by a gap
As far as perturbation theory is valid, the existence of the integer quantum Hall effect after interactions are turned on is intimately tied to the question of whether the incompressible nature of the state due to the energy gap between Landau levels survives in the interacting theory
We have not explored the blown up solutions of the D5 brane from the D5 brane point of view where it would be a non-Abelian configuration of D5 branes
Summary
We shall study D5 and D7 probe branes at finite temperature and density. We will embed them in the asymptotically AdS5 × S5 black hole background using coordinates where the. If the interactions are not fully SU(4) invariant, but are symmetric under SO(3) × SU(2) instead, this state would break both the SO(3) and SU(2) symmetries. What is more, it is not the unique choice for a quarter filled state. (t, x, y, z, r) are coordinates of the Poincare patch of AdS5 and h(r) rh r4. The world volume coordinates of our probe branes will be as given in the table above
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
