The Nicolai-map approach to supersymmetry

TL;DR

The paper reviews the Nicolai map, a nonlocal transformation in supersymmetric theories, highlighting recent progress in its construction and applications across various models after decades of dormancy.

Contribution

It provides a modern perspective on the Nicolai map, summarizing recent advances in its construction and understanding in quantum mechanics and super Yang-Mills theories.

Findings

Recent technical progress in constructing the Nicolai map.

Deeper insight into the nature of the Nicolai map.

Applications to quantum mechanics and super Yang-Mills theories.

Abstract

In 1980 Hermann Nicolai proposed a characterization of supersymmetric theories that became known as the Nicolai map. This is a particular nonlocal and nonlinear field transformation, whose perturbative expansion is given by fermion-line trees with bosonic leaves. Quantum correlation functions can by evaluated using the inversely transformed fields in the free theory. After initial promise and excitement (fuelling the author's PhD work!), the subject all but fell dormant for 35 years. Recently however, technical progress in the construction as well as a deeper insight into the nature of the map have been achieved, from quantum mechanics to super Yang-Mills in various dimensions. I will present the Nicolai map from this modern perspective and touch on some of the current developments.