Holographic non-Fermi liquids at large $d$

TL;DR

This paper investigates fermion two-point functions in a charged black brane background within large $d$ dimensions, revealing a locally critical self-energy and expanding the temperature regime for analysis, with more tractable calculations.

Contribution

It introduces a large $d$ framework for analyzing holographic non-Fermi liquids, highlighting new scaling behaviors and analytical methods not present in lower dimensions.

Findings

Emergence of locally critical fermion self-energy at large $d$

Expanded temperature regime for valid results

Analytical tractability of fermionic correlators in large $d$

Abstract

Motivated by the results of Dynamical Mean Field Theory, we study the two-point function of fermions moving in a charged black brane background in $AdS_{d+1}$ in the limit of large $d$. We observe the emergence of a locally critical form of the fermion self-energy, with a strongly constrained range of possible scaling behaviors at large $d$. Novelties compared to the analysis in $d=3,4$ include an enlarged regime of temperatures where the results apply, and the analytical tractability of the calculations.