A proof of the continuous Dyson-Maleev representation

TL;DR

This paper rigorously proves key integral identities underlying continuous Dyson-Maleev representations of supersymmetric non-linear sigma models, confirming their non-perturbative exactness.

Contribution

It provides a rigorous mathematical foundation for the integral identities essential to continuous Dyson-Maleev representations.

Findings

Established key integral identities for hermitian symmetric spaces.

Confirmed the non-perturbative exactness of continuous Dyson-Maleev representations.

Strengthened the mathematical basis for supersymmetric sigma models.

Abstract

Recently Ivanov and Skvortsov introduced continuous Dyson-Maleev (DM) representations of supersymmetric non-linear sigma models and motivated that these representations are non-perturbatively exact. Basic to all continuous DM representations of this kind are certain identities for integrals over hermitian (super)symmetric spaces. We establish these basic identities rigorously in the non-super case.