Interacting Fractons in 2+1-Dimensional Quantum Field Theory

TL;DR

This paper investigates a 2+1D quantum field theory of weakly interacting fractons and fermions, revealing a non-flowing fracton-fermion coupling due to an emergent symmetry, and discusses renormalization and finite-temperature effects.

Contribution

It introduces a perturbative analysis of interacting fractons in 2+1D, showing the coupling's non-flow and providing insights into regularization and finite-temperature behavior.

Findings

Fracton-fermion coupling does not flow under RG due to emergent symmetry.

Computed 1-loop self energies and interaction vertex corrections.

Discussed regularization, renormalization, and finite-temperature effects.

Abstract

We analyze, in perturbation theory, a theory of weakly interacting fractons and non-relativistic fermions in a 2+1 dimensional Quantum Field Theory. In particular we compute the 1-loop corrections to the self energies and interaction vertex, and calculate the associated 1-loop Renormalization Group flows of the coupling constants. Surprisingly, we find that the fracton-fermion coupling does not flow due to an emergent coordinate-dependent symmetry of the effective Lagrangian, making this model a well-defined quantum field theory. We provide additional discussions on the regularization and renormalization of interacting fractonic theories, as well as both qualitative and quantitative remarks regarding the theory at finite temperature and finite chemical potential.