The $H^{2|2}$ monotonicity theorem revisited

TL;DR

This paper revisits the $H^{2|2}$ monotonicity theorem using supersymmetric localization, providing an alternative proof that avoids probabilistic couplings and introduces new correlation inequalities in statistical physics.

Contribution

It offers a novel proof of the $H^{2|2}$ monotonicity theorem using supersymmetric methods, expanding the theoretical toolkit in statistical physics.

Findings

Derived variational and convex correlation inequalities

Provided an alternative proof of the $H^{2|2}$ monotonicity theorem

Revealed new applications of supersymmetric localization

Abstract

We use supersymmetric localization and integration by parts to derive variational and convex correlation inequalities in statistical physics. As a primary application, we give an alternative proof of the monotonicity theorem for the $H^{2|2}$ supersymmetric hyperbolic sigma model. This recovers a result of Poudevigne without relying on probabilistic couplings.