Non relativistic diffeomorphism and the geometry of the fractional quantum Hall effect

TL;DR

This paper demonstrates that a method for constructing nonrelativistic diffeomorphism invariant theories naturally connects with the geometry underlying the fractional quantum Hall effect, reproducing key physical quantities like Hall viscosity.

Contribution

It shows that gauging Galilean symmetry in nonrelativistic theories naturally reproduces geometric features of the FQHE, such as Hall viscosity and Wen-Zee shift.

Findings

Covariant derivatives reproduce Hall viscosity

Connection between gauged Galilean symmetry and FQHE geometry

Reproduction of Wen-Zee shift from the method

Abstract

We show that our recently proposed method\cite{BMM1,BMM2,BMM3,BM4} of constructing nonrelativistic diffeomorphism invariant field theories by gauging the Galilean symmetry provides a natural connection with the geometry of the fractional quantum Hall effect (FQHE). Specifically, the covariant derivative that appears on gauging, exactly reproduces the form that yields the Hall viscosity and Wen-Zee shift \cite{CYF}.