Fractons, non-Riemannian Geometry, and Double Field Theory

TL;DR

This paper explores fracton physics through the lens of Double Field Theory, revealing geometric origins of immobility and degeneracy, and connecting gauge theories to elasticity, phonons, and polaron phenomena.

Contribution

It introduces a geometric framework linking fractons to non-Riemannian backgrounds in Double Field Theory, unifying gauge fields with elasticity and revealing new physical insights.

Findings

Fractons are related to non-Riemannian backgrounds in Double Field Theory.

Pure gauge theories reduce to elasticity-like models coupling photons and phonons.

Predictions include effective mass generation for particles and saturation velocities in fractonic regimes.

Abstract

We initiate a systematic study of fracton physics within the geometric framework of Double Field Theory. We ascribe the immobility and large degeneracy of the former to the non-Riemannian backgrounds of the latter, in terms of generalised geodesics and infinite-dimensional isometries. A doubled pure Yang-Mills or Maxwell theory reduces to an ordinary one coupled to a strain tensor of elasticity theory, and thus rather remarkably provides a unifying description of photons and phonons. Upon a general Double Field Theory background, which consists of Riemannian and non-Riemannian subspaces, the dual photon-phonon pair becomes fractonic over the non-Riemannian subspace. When the elasticity displacement vector condenses, minimally coupled charged particles acquire an effective mass even in the purely Riemannian case, yielding predictions for polaron physics and time crystals. Furthermore, the immobility of neutral particles along the non-Riemannian directions is lifted to a saturation velocity for charged particles. Utilising the differential geometry of Double Field Theory we also present curved spacetime extensions which exhibit general covariance.