Universal form of the Nicolai map

TL;DR

This paper presents a universal formula for the Nicolai map in supersymmetric theories, enabling explicit construction of the nonlocal bosonic theories obtained by integrating out fermionic variables, applicable to scalar and gauge theories.

Contribution

It introduces a universal, explicit formula for the Nicolai map and its inverse, valid for scalar superfield theories and supersymmetric gauge theories, advancing the understanding of supersymmetric transformations.

Findings

Universal formula for the Nicolai map and its inverse

Applicable to scalar superfield and gauge theories

Facilitates explicit construction of bosonic theories from supersymmetric models

Abstract

The nonlocal bosonic theory obtained from integrating out all anticommuting and auxiliary variables in a globally supersymmetric theory is characterized by the Nicolai map. The latter is generated by a coupling flow functional differential operator, which can be canonically constructed when the supersymmetry is realized off-shell. Given any scalar superfield theory, we present a universal formula for both the Nicolai map and its inverse in terms of an ordered exponential of the integrated coupling flow operator. We demonstrate that our formula also holds for supersymmetric gauge theories.