Towards a holographic marginal Fermi liquid

TL;DR

The paper builds an explicit infinite class of 2+1d field theories with defect sectors coupled to parity-preserving supersymmetric Chern-Simons theories, realized holographically via lattices of M2-branes (and D2-branes in the IIA limit). By computing defect operator dimensions from KK spectra on M2' worldvolumes, it identifies a Δ = 1 fermionic operator suitable for coupling to a semi-holographic Fermi surface, yielding marginal Fermi liquid behavior in the large-N regime. It further analyzes backreaction effects and weak-coupling radiative corrections, finding potential IR local criticality in controlled backreacted setups but highlighting challenges at finite N and possible obstructions from inter-defect couplings, with CS dynamics offering possible protection. Overall, the work provides a concrete, microscopically motivated holographic route to local quantum criticality and MFL behavior, outlining both its robustness and its limits in finite-N and weak-coupling regimes.

Abstract

We present an infinite class of 2+1 dimensional field theories which, after coupling to semi-holographic fermions, exhibit strange metallic behavior in a suitable large $N$ limit. These theories describe lattices of hypermultiplet defects interacting with parity-preserving supersymmetric Chern-Simons theories with $U(N) \times U(N)$ gauge groups at levels $\pm k$. They have dual gravitational descriptions in terms of lattices of probe M2 branes in $AdS_4 \times S^7/Z_k$ (for $N \gg 1, N \gg k^5$) or probe D2 branes in $AdS_4 \times CP^3$ (for $N \gg k \gg 1, N \ll k^5$). We discuss several challenges one faces in maintaining the success of these models at finite $N$, including backreaction of the probes in the gravity solutions and radiative corrections in the weakly coupled field theory limit.