Numerical Stochastic Perturbation Theory around instantons

TL;DR

This paper extends Numerical Stochastic Perturbation Theory to instanton backgrounds, demonstrating its application to quantum mechanics and computing perturbative expansions around non-trivial vacua.

Contribution

It introduces NSPT expansions around instantons and applies this method to the double well potential, advancing the understanding of perturbations around non-trivial vacua.

Findings

Computed perturbative expansions of ground-state energy splitting.

Reproduced known two-loop results.

Presented progress on higher-order computations.

Abstract

Numerical Stochastic Perturbation Theory (NSPT) has over the years proved to be a valuable tool, in particular being able to reach unprecedented orders for Lattice Gauge Theories, whose perturbative expansions are notoriously cumbersome. One of the key features of the method is the possibility to expand around non-trivial vacua. While this idea has been around for a while, and it has been implemented in the case of the (non-trivial) background of the Schr\"odinger functional, NSPT expansions around instantons have not yet been fully worked out. Here we present computations for the double well potential in quantum mechanics. We compute a few orders of the expansion of the ground-state energy splitting in the one-instanton sector. We discuss how (already) known two-loop results are reproduced and present the current status of higher-order computations.