p-wave Holographic Superconductors and five-dimensional gauged Supergravity

Understand

We explore five-dimensional ${\cal N}=4$ $SU(2)\times U(1)$ and ${\cal N}=8$ SO(6) gauged supergravities as frameworks for condensed matter applications.

• These theories contain charged (dilatonic) black holes and 2-forms which have non-trivial quantum numbers with respect to U(1) subgroups of SO(6).
• A question of interest is whether they also contain black holes with two-form hair with the required asymptotic to give rise to holographic superconductivity.
• We first consider the ${\cal N}=4$ case, which contains a complex two-form potential $A_{\mu\nu}$ which has U(1) charge $\pm 1$.