Generalized conformal maps as classical symmetries of Yang-Mills fields

TL;DR

This paper demonstrates that certain generalized maps, including self-dual and causal morphisms, act as classical symmetries of Yang-Mills fields, extending conformal symmetry to a broader class of transformations in complex four-dimensional space.

Contribution

It introduces a new class of symmetries called self-dual and causal morphisms that generalize conformal transformations for Yang-Mills fields, including supersymmetric cases.

Findings

Self-dual morphisms are symmetries of anti-self-dual Yang-Mills equations.

Supersymmetric causal morphisms preserve solutions of N=3 supersymmetric Yang-Mills.

Modified causal morphisms form symmetries of ordinary Yang-Mills equations.

Abstract

We show that a class of previously defined maps, called self-dual and causal morphisms, form classical symmetries of Yang-Mills fields in four complex dimensions. These maps generalize conformal transformations, and admit a nonlocal pullback connection that preserves the equations of the theory. First it is shown that self-dual morphisms form symmetries of the anti-self-dual Yang-Mills equations under this pullback. Then a supersymmetric generalization of causal morphisms is defined, which preserves solutions of the field equations for N=3 supersymmetric Yang-Mills theory. As a special case, this implies that a modified definition of causal morphisms form symmetries for the ordinary Yang-Mills field equations.