Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story

TL;DR

This paper explores the generalized electromagnetic theory for subdimensional particles like fractons in 3+1D spin liquids, extending classical electromagnetism concepts to tensor gauge fields and their unique particle interactions.

Contribution

It develops the basic electromagnetic framework for subdimensional particles coupled to tensor gauge fields, including electrostatics, potentials, and Maxwell equations, highlighting both similarities and differences with conventional electromagnetism.

Findings

Generalized electrostatic fields for subdimensional particles

Modified Maxwell equations for tensor electromagnetism

Biot-Savart laws adapted to subdimensional particle dynamics

Abstract

It has recently been shown that there exists a class of stable gapless spin liquids in 3+1 dimensions described by higher rank tensor U(1) gauge fields, giving rise to an emergent tensor electromagnetism. The tensor gauge field of these theories couples naturally to subdimensional particles (such as fractons), which are restricted by gauge invariance to move only along lower-dimensional subspaces of the system. We here work out some of the basic generalized electromagnetic properties of subdimensional particles coupled to tensor electromagnetism, such as generalized electrostatic fields, potential formulations, Lorentz forces, Maxwell equations, and Biot-Savart laws. Some concepts from conventional electromagnetism will carry over directly, while others require significant modification.