Unified genus-1 potential and a parametric perturbative/nonperturbative relation

TL;DR

This paper introduces a unified approach to genus-1 anharmonic potentials, deriving a parametric perturbative/nonperturbative relation that captures all instanton effects from perturbative data across all parameters.

Contribution

It develops a comprehensive parametric P/NP relation for genus-1 potentials, enabling nonperturbative insights solely from perturbative expansions, extending known results.

Findings

Perturbative expansion suffices to generate all nonperturbative information.

Reproduces known cubic and quartic anharmonic potential results.

Develops nonperturbative functions from perturbative data for real and complex instantons.

Abstract

We study a parametric deformation of the unified genus-1 anharmonic potential and derive a parametric form of perturbative/nonperturbative (P/NP) relation, applicable across all parameter values. We explicitly demonstrate that the perturbative expansion around the perturbative saddle is sufficient to generate all the nonperturbative information in these systems. Our results confirm the known results in the literature, where the cubic and quartic anharmonic potentials are reproduced under extreme parameter values, and go beyond these known results by developing the nonperturbative function of real and complex instantons solely from perturbative data.