Flow Equation for Supersymmetric Quantum Mechanics

TL;DR

This paper develops a supersymmetric functional renormalization group approach to quantum mechanics, accurately computing energy levels in nonperturbative regimes while maintaining off-shell supersymmetry.

Contribution

It introduces an exact off-shell supersymmetric flow equation and solves it nonperturbatively, providing precise energy calculations for supersymmetric quantum systems.

Findings

First excited state energy determined within 1% error

Applicable to a wide range of couplings including nonperturbative regimes

Maintains off-shell supersymmetry throughout the analysis

Abstract

We study supersymmetric quantum mechanics with the functional RG formulated in terms of an exact and manifestly off-shell supersymmetric flow equation for the effective action. We solve the flow equation nonperturbatively in a systematic super-covariant derivative expansion and concentrate on systems with unbroken supersymmetry. Already at next-to-leading order, the energy of the first excited state for convex potentials is accurately determined within a 1% error for a wide range of couplings including deeply nonperturbative regimes.