Fermionic operator mixing in holographic p-wave superfluids

We use gauge-gravity duality to compute spectral functions of fermionic operators in a strongly-coupled defect field theory in p-wave superfluid states. The field theory is (3+1)-dimensional $ \mathcal{N} = 4 $ supersymmetric SU(Nc) Yang-Mills theory, in the ’t Hooft limit and with large coupling, coupled to two massless flavors of (2+1)-dimensional $ \mathcal{N} = 4 $ supersymmetric matter. We show that a sufficiently large chemical potential for a U(1) subgroup of the global SU(2) isospin symmetry triggers a phase transition to a p-wave superfluid state, and in that state we compute spectral functions for the fermionic superpartners of mesons valued in the adjoint of SU(2) isospin. In the spectral functions we see the breaking of rotational symmetry and the emergence of a Fermi surface comprised of isolated points as we cool the system through the superfluid phase transition. The dual gravitational description is two coincident probe D5-branes in AdS5 × S5 with non-trivial worldvolume SU(2) gauge fields. We extract spectral functions from solutions of the linearized equations of motion for the D5-branes’ worldvolume fermions, which couple to one another through the worldvolume gauge field. We develop an efficient method to compute retarded Green’s functions from a system of coupled bulk fermions. We also perform the holographic renormalization of free bulk fermions in any asymptotically Euclidean AdS space.