Diagnostic Tomography of Applied Holography

TL;DR

This paper explores a holographic approach to understanding the behavior of multi-species Fermi gases in one dimension, revealing boundary dynamics that challenge the notion of a full holographic duality.

Contribution

It introduces a 'tomographic' holographic framework for Fermi gases and clarifies the topological nature of the bulk theory, emphasizing boundary dynamics over bulk dynamics.

Findings

Boundary dynamics dominate due to topological bulk nature

Formal holographic correspondence does not imply a genuine duality

Framework applies to strongly interacting multi-species Fermi gases

Abstract

The single-particle behavior in $d\geq 1$-dimensional Fermi gases with a large number $N$ of species and strong short-range $s$-wave scattering is discussed in the $2d$ 'tomographic' framework of a (pseudo)holographic correspondence with a certain $3d$ gravity of the $AdS_3$ type. However, due to the intrinsically topological nature of such a bulk theory its dynamics reduces to a purely boundary one and so, akin to its $SYK/AdS_2$ counterpart, this formal correspondence neither represents a genuine case of, nor endorses the hypothetical generalized holographic duality.