Pairing instabilities of Dirac fermions at strong coupling
In this talk we will discuss electron systems with a Lorentz-invariant dispersion relation and particle-hole symmetry at low energies, but with microscopic physics deviating strongly from the non-interacting Dirac fermions. We will consider the Berry connection in such systems and explore if it is determined solely by the particle-hole symmetry, without regard to the details of the dispersion relation. Within a perturbation theory powered by a gauge/gravity duality, we will investigate what happens in the presence of particle-particle and particle-hole pairing channels. We will also discuss the implications for the bilayer systems at half-filling.