On duality between Cosserat elasticity and fractons

TL;DR

This paper introduces a dual formulation of Cosserat elasticity, mapping local displacement and orientation to gauge fields, and explores the associated gauge theories, defects, and effects of curved space.

Contribution

It presents a novel duality between Cosserat elasticity and gauge theories, linking elastic degrees of freedom to vector-valued one-form and U(1) gauge fields.

Findings

Dual formulation of Cosserat elasticity using gauge fields

Analysis of defect matter and gauge coupling in curved space

Insights into degrees of freedom in the dual gauge theories

Abstract

We present a dual formulation of the Cosserat theory of elasticity. In this theory a local element of an elastic body is described in terms of local displacement and local orientation. Upon the duality transformation these degrees of freedom map onto a coupled theory of a vector-valued one-form gauge field and an ordinary $U(1)$ gauge field. We discuss the degrees of freedom in the corresponding gauge theories, the defect matter and coupling to the curved space.