Complex Langevin Dynamics and Supersymmetric Quantum Mechanics

TL;DR

This paper investigates the use of the complex Langevin method to study dynamical supersymmetry breaking in supersymmetric quantum mechanics models with complex actions, where traditional methods fail due to the sign problem.

Contribution

It demonstrates that the complex Langevin method can reliably determine supersymmetry breaking in models with complex actions, overcoming limitations of importance sampling.

Findings

Complex Langevin successfully evades the sign problem.

The method accurately predicts supersymmetry breaking or preservation.

Simulations confirm the reliability of complex Langevin in these models.

Abstract

Using complex Langevin method we probe the possibility of dynamical supersymmetry breaking in supersymmetric quantum mechanics models with complex actions. The models we consider are invariant under the combined operation of parity and time reversal, in addition to supersymmetry. When actions are complex traditional Monte Carlo methods based on importance sampling fail. Models with dynamically broken supersymmetry can exhibit sign problem due to the vanishing of the partition function. Complex Langevin method can successfully evade the sign problem. Our simulations suggest that complex Langevin method can reliably predict the absence or presence of dynamical supersymmetry breaking in these one-dimensional models with complex actions.