Simplifying 4d $\mathcal{N}=3$ Harmonic Superspace

TL;DR

This paper simplifies the quantization of super Yang-Mills in 4d N=3 harmonic superspace, providing easier computational tools and demonstrating finiteness at 1-loop with explicit calculations.

Contribution

It introduces a simplified quantization method with new propagators and Feynman rules, and verifies the finiteness of the theory at 1-loop.

Findings

Divergences do not appear at 1-loop and beyond.

Explicit 1-loop finite contribution computed from a 4-point diagram.

Simplified propagators and rules facilitate calculations.

Abstract

We quantize super Yang-Mills action in $\mathcal{N}=3$ harmonic superspace using "Fermi-Feynman" gauge and also develop the background field formalism. This leads to simpler propagators and Feynman rules that are useful in performing explicit calculations. The superspace rules are used to show that divergences do not appear at 1-loop and beyond. We also compute a finite contribution to the effective action from a 4-point diagram at 1-loop, which matches the expected covariant result.