The Noncommutative S-Matrix

TL;DR

This paper explores the S-matrix of noncommutative gauge theories, demonstrating that despite nonlocal features and complex singularities, tree-level and one-loop amplitudes can be systematically computed using adapted on-shell techniques.

Contribution

It extends on-shell recursion and unitarity methods to noncommutative gauge theories, revealing a simplified S-matrix structure similar to commutative N=4 SYM.

Findings

Tree-level amplitudes obtained via BCFW recursion in noncommutative theories.

A complete basis of master integrals for one-loop amplitudes, larger than in ordinary theories.

Noncommutative N=4 SYM has a structurally simple S-matrix like the ordinary theory.

Abstract

As a simple example of how recently developed on-shell techniques apply to nonlocal theories, we study the S-matrix of noncommutative gauge theories. In the complex plane, this S-matrix has essential singularities that signal the nonlocal behavior of the theory. In spite of this, we show that tree-level amplitudes may be obtained by BCFW type recursion relations. At one loop we find a complete basis of master integrals (this basis is larger than the corresponding basis in the ordinary theory). Any one-loop noncommutative amplitude may be written as a linear combination of these integrals with coefficients that we relate to products of tree amplitudes. We show that the noncommutative N=4 SYM theory has a structurally simple S-matrix, just like the ordinary N=4 SYM theory.