N=4 super-Yang-Mills in LHC superspace. Part I: Classical and quantum theory

TL;DR

This paper introduces a Lorentz harmonic chiral superspace formulation of N=4 super-Yang-Mills theory, simplifying the handling of auxiliary fields and manifesting half of the supersymmetry, with implications for quantum and classical analyses.

Contribution

It presents a new LHC superspace approach for N=4 SYM, closely related to twistor methods but using Lorentz harmonic variables for efficiency.

Findings

Derived Feynman rules in coordinate space.

Showed the LHC formulation's similarity to N=2 harmonic superspace.

Established a foundation for studying correlation functions in the twin paper.

Abstract

We present a formulation of the maximally supersymmetric N=4 gauge theory in Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor formulation of the theory but employs the simpler notion of Lorentz harmonic variables. They parametrize a two-sphere and allow us to handle efficiently infinite towers of higher-spin auxiliary fields defined on ordinary space-time. In this approach the chiral half of N=4 supersymmetry is manifest. The other half is realized non-linearly and the algebra closes on shell. We give a straightforward derivation of the Feynman rules in coordinate space. We show that the LHC formulation of the N=4 super-Yang-Mills theory is remarkably similar to the harmonic superspace formulation of the N=2 gauge and hypermultiplet matter theories. In the twin paper arXiv:1601.06804 we apply the LHC formalism to the study of the non-chiral multipoint correlation functions of the N=4 stress-tensor supermultiplet.