Supersymmetry and Nonreciprocity

TL;DR

This paper demonstrates that nonreciprocal stochastic theories, common in non-equilibrium phenomena, can be mapped onto supersymmetric quantum field theories, extending previous work on reciprocal systems.

Contribution

It introduces a supersymmetric framework for nonreciprocal stochastic theories, generalizing the Parisi-Sourlas approach to non-Hermitian, nonreciprocal systems.

Findings

Nonreciprocal theories can be mapped to supersymmetric quantum field theories.

The resulting theories are generally non-Hermitian.

This generalizes the Parisi-Sourlas framework to nonreciprocal systems.

Abstract

Nonreciprocal theories are used to model a broad array of non-equilibrium phenomena found in nature ranging from biological systems like networks of neurons to the behavior of overflowing water fountains. This includes systems broadly classified as active matter systems. We show that the stochastic theories which describe nonreciprocal interactions can be mapped into quantum field theories described by a supersymmetric action with a single supercharge. The theories are generically non-Hermitian. This generalizes the past work of Parisi and Sourlas on reciprocal theories, which model systems with interactions derived from potentials.