Holographic Fermionic Fixed Points in d=3

TL;DR

This paper develops a string theory holographic model for 2+1-dimensional fermions, exploring different symmetry-breaking phases and their electromagnetic responses, including a quantized Chern-Simons term, relevant for strongly interacting systems like graphene.

Contribution

It introduces a top-down holographic model with probe D7-branes capturing parity and time reversal symmetry effects in 2+1D fermionic systems, including novel solutions with and without gaps.

Findings

Identified three distinct solutions with different symmetry properties.

Demonstrated the emergence of a quantized Chern-Simons response in the gapped phase.

Computed quantum corrections to the Chern-Simons response in the gapless phase.

Abstract

We present a top-down string theory holographic model of strongly interacting relativistic 2+1-dimensional fermions, paying careful attention to the discrete symmetries of parity and time reversal invariance. Our construction is based on probe $D7$-branes in $AdS_5 \times S^5$, stabilized by internal fluxes. We find three solutions, a parity and time reversal invariant conformal field theory which can be viewed as a particular deformation of Coulomb interacting graphene, a parity and time reversal violating but gapless field theory and a system with a parity and time reversal violating charge gap. We show that the Chern-Simons-like electric response function, which is generated perturbatively at one-loop order by parity violating fermions and which is protected by a no-renormalization theorem at orders beyond one loop, indeed appears with the correctly quantized coefficient in the charge gapped theory. In the gapless parity violating solution, the Chern-Simons response function obtains quantum corrections which we compute in the holographic theory.