Dual representation for 1+1 dimensional fermions interacting with 3+1 dimensional U(1) gauge fields

TL;DR

This paper introduces a dual representation for 1+1D fermions interacting with 3+1D U(1) gauge fields, enabling Monte Carlo simulations at arbitrary chemical potentials by overcoming the complex action problem.

Contribution

The authors develop a dual formulation mapping fermions to dimers and loops, and gauge fields to surfaces, allowing simulations without the complex action issue.

Findings

Dual variables eliminate the complex action problem.

Monte Carlo simulations are feasible at any chemical potential.

The dual representation captures the system's physics effectively.

Abstract

We study a system of nanowires, i.e., the theory of 1+1 dimensional massless fermions interacting with 3+1 dimensional U(1) gauge fields. When allowing for non-zero chemical potentials, this system has a complex action problem in the conventional formulation. We show that the partition sum can be mapped to a dual representation where the fermions correspond to dimers and oriented loops on 2-dimensional planes embedded in 4 dimensions. The dual degrees of freedom for the gauge fields are surfaces that either are closed or bounded by the fermion loops. In terms of the dual variables the complex action problem is overcome and Monte Carlo simulations are possible for arbitrary chemical potentials.