N=4 Yang--Mills theory as a complexification of the N=2 theory

TL;DR

This paper demonstrates how complexifying the twisted N=2 theory enables the derivation of the N=4 Yang--Mills theory in its third twist, establishing a direct correspondence between their fields through complexification.

Contribution

It introduces a novel complexification approach to connect N=2 and N=4 Yang--Mills theories, providing a new perspective on their field structures and relationships.

Findings

Established a one-to-one correspondence between N=2 and N=4 fields.

Used imaginary gauge symmetry to eliminate scalars and form gauge covariant components.

Extended complexification method to topological 2d-gravity and sigma models.

Abstract

A complexification of the twisted $\N=2$ theory allows one to determine the N=4 Yang--Mills theory in its third twist formulation. The imaginary part of the gauge symmetry is used to eliminate two scalars fields and create gauge covariant longitudinal components for the imaginary part of the gauge field. The latter becomes the vector field of the thirdly twisted $\N=4$ theory. Eventually, one gets a one to one correspondence between the fields of both theories. Analogous complexifications can be done for topological 2d-gravity and topological sigma models.