Non-Abelian Gauged Fracton Matter Field Theory: New Sigma Models, Superfluids and Vortices

TL;DR

This paper introduces a novel class of non-abelian higher-rank tensor gauge theories with fractonic matter, explores their phase transitions to superfluid phases, and investigates non-abelian vortices with complex interactions.

Contribution

It develops new non-abelian gauged fracton gauge theories and constructs associated Sigma models, extending previous models to include non-commutative symmetries and vortex dynamics.

Findings

Derived a new class of non-abelian tensor gauge theories with fractonic matter.

Established phase transitions between disordered gauge phases and ordered superfluid phases.

Analyzed non-abelian vortices with non-commutative interactions and their mathematical properties.

Abstract

By gauging a higher-moment polynomial degree global symmetry and a discrete charge conjugation (i.e., particle-hole) symmetry coupled to matter fields (two symmetries mutually non-commutative), we derive a new class of higher-rank tensor non-abelian gauge field theory with dynamically gauged fractonic matter fields: Non-abelian gauged fractons interact with a hybrid class of higher-rank (symmetric or generic non-symmetric) tensor gauge theory and anti-symmetric tensor topological field theory, generalizing [arXiv:1909.13879, 1911.01804]. We also apply a quantum phase transition similar to that between insulator v.s. superfluid/superconductivity (U(1) symmetry disordered phase described by a topological gauge theory or a disordered Sigma model v.s. U(1) global/gauge symmetry-breaking ordered phase described by a Sigma model with a U(1) target space underlying Goldstone modes): We can regard our tensor gauge theories as disordered phases, and we transient to their new ordered phases by deriving new Sigma models in continuum field theories. While one low energy theory is captured by degrees of freedom of rotor or scalar modes, another side of low energy theory has vortices and superfluids -- we explore non-abelian vortices (two types of vortices mutually interacting non-commutatively beyond an ordinary group structure) and their Cauchy-Riemann relation.