Symmetries of the N=4 SYM S-matrix

TL;DR

This paper proves that the N=4 SYM S-matrix maintains superconformal invariance at all loop orders under a generalized CSW approach, and introduces a regularization that preserves this symmetry.

Contribution

It demonstrates superconformal invariance of the N=4 SYM S-matrix at all loops assuming a CSW generalization, and proposes a regularization preserving this symmetry.

Findings

Superconformal invariance holds at all loop orders under the assumptions.

A new regularization preserves superconformal symmetry in IR-safe quantities.

The results are exact for tree-level and one-loop MHV amplitudes without assumptions.

Abstract

Under the assumption of a CSW generalization to loop amplitudes in N=4 SYM, (1) We prove that, formally the S-matrix is superconformal invariant to any loop order, and (2) We argue that superconformal symmetry survives regularization. More precisely, IR safe quantities constructed from the S-matrix are superconformal covariant. The IR divergences are regularized in a new holomorphic anomaly friendly regularization. The CSW prescription is known to be valid for all tree level amplitudes and for one loop MHV amplitudes. In these cases, our formal results do not rely on any assumptions.