Shear Viscosity of a Non-Relativistic Conformal Gas in Two Dimensions

TL;DR

The paper investigates the shear viscosity to entropy density ratio $\eta/s$ for a two-dimensional, non-relativistic conformal Fermi gas. Using leading-order effective field theory with a contact interaction, it shows that in $d=2$ at zero binding energy ($B=0$) the two-body scattering amplitude vanishes for $E>0$, effectively rendering the system free and driving $\eta/s$ to infinity. The gravitational analysis within the NR AdS/CFT framework reveals that for $d=2$ the Schrödinger-invariant background yields only the free-fermion boundary behavior ($\nu=0$), causing the gravity dual to degenerate to the free limit and precluding a weakly coupled holographic dual at unitarity. Together, these results imply that, unlike certain higher-dimensional cases, the 2D unitary Fermi gas is unlikely to possess a weakly interacting gravity dual, motivating the search for genuinely strongly interacting NRCFTs in two dimensions.

Abstract

The shear viscosity, eta, of a fermi gas with non-relativistic conformal symmetry in two spatial dimensions is investigated. We find that eta/s, s being the entropy density, diverges as a gas of free particles in this system. It is in contrast to the eta/s=1/(4 pi) found using non-relativistic AdS/CFT correspondence, which requires a strongly interacting CFT. It implies the unitary fermi gas in two spatial dimensions is not likely to have a weakly interacting gravity dual.

Figures (1)

• Figure 1: Leading order diagrams for two fermion scattering.