Minimally packed phases in holography

Understand

We numerically construct asymptotically AdS black brane solutions of $D=4$ Einstein-Maxwell theory coupled to a pseudoscalar.

• The solutions are holographically dual to $d=3$ CFTs at finite chemical potential and in a constant magnetic field, which spontaneously break translation invariance leading to the spontaneous formation of abelian and momentum magnetisation currents flowing around the plaquettes of a periodic Bravais lattice.
• We analyse the three-dimensional moduli space of lattice solutions, which are generically oblique, and show, for a specific value of the magnetic field, that the free energy is minimised by the triangular lattice, associated with minimal packing of circles in the plane.
• We show that the average stress tensor for the thermodynamically preferred phase is that of a perfect fluid and that this result applies more generally to spontaneously generated periodic phases.