Deconstructing zero: resurgence, supersymmetry and complex saddles

TL;DR

This paper explores how resurgence links vanishing perturbative expansions in supersymmetric theories to non-perturbative fluctuations, revealing saddle point cancellations and dominance that determine supersymmetry breaking.

Contribution

It demonstrates the connection between zero perturbative series and non-perturbative sectors via resurgence, highlighting saddle point roles in supersymmetry.

Findings

Vanishing perturbative expansions relate to non-perturbative fluctuations.

Supersymmetry unbroken: cancellation between real and complex saddles.

Supersymmetry broken: dominance of complex saddles.

Abstract

We explain how a vanishing, or truncated, perturbative expansion, such as often arises in semi-classically tractable supersymmetric theories, can nevertheless be related to fluctuations about non-perturbative sectors via resurgence. We also demonstrate that, in the same class of theories, the vanishing of the ground state energy (unbroken supersymmetry) can be attributed to the cancellation between a real saddle and a complex saddle (with hidden topological angle pi), and positivity of the ground state energy (broken supersymmetry) can be interpreted as the dominance of complex saddles. In either case, despite the fact that the ground state energy is zero to all orders in perturbation theory, all orders of fluctuations around non-perturbative saddles are encoded in the perturbative E(N, g). We illustrate these ideas with examples from supersymmetric quantum mechanics and quantum field theory.