New N=4 SYM Path Integral

TL;DR

This paper reformulates the N=4 supersymmetric Yang-Mills path integral using Lorentz covariant spinor helicity formalism, aiming to simplify calculations while preserving supersymmetry.

Contribution

It introduces a new variable change in the path integral that makes Lorentz and supersymmetry properties manifest, potentially simplifying unitarity-based computations.

Findings

Quadratic and cubic action parts have manifest supersymmetry in new variables.

Terms breaking dynamical supersymmetry are argued to cancel out.

The reformulation suggests simpler unitarity rules for N=4 SYM.

Abstract

Using Lorentz covariant spinor helicity formalism we reorganize the unitary scalar superfield light-cone path integral for the N=4 supersymmetric Yang-Mills theory. In new variables in the chiral Fourier superspace the quadratic and cubic parts of the classical action have manifest Lorentz, kinematical and dynamical supersymmetry, with the exception of terms which contribute only to the contact terms in the supergraphs with propagators shrinking to a point. These terms have the same structure as supergraphs with quartic light-cone vertices, which break dynamical supersymmetry. We present evidence that all complicated terms breaking dynamical supersymmetry have to cancel and therefore can be omitted. It is plausible that the new form of the path integral leads to a set of relatively simple unitarity based rules with manifest N=4 supersymmetry.