The Next-to-Simplest Quantum Field Theories

TL;DR

This paper introduces new recursion relations for tree-level amplitudes in N=1 and N=2 gauge theories, revealing their structural similarities to pure Yang-Mills and identifying conditions for simplified one-loop amplitudes.

Contribution

It presents novel on-shell recursion relations for N=1 and N=2 gauge theories and characterizes conditions for one-loop amplitude simplifications involving higher-order Indices.

Findings

One-loop amplitudes in certain N=2 theories are as simple as in N=4.

Some non-supersymmetric theories are free of bubble diagrams at one-loop.

New examples of theories with only box diagrams at one-loop are provided.

Abstract

We describe new on-shell recursion relations for tree-amplitudes in N=1 and N=2 gauge theories and use these to show that the structure of the S-matrix in pure N=1 and N=2 gauge theories resembles that of pure Yang-Mills. We proceed to study gluon scattering in gauge theories coupled to matter in arbitrary representations. The contribution of matter to individual bubble and triangle coefficients can depend on the fourth and sixth order Indices of the matter representation respectively. So, the condition that one-loop amplitudes be free of bubbles and triangles can be written as a set of linear Diophantine equations involving these higher-order Indices. These equations simplify for supersymmetric theories. We present new examples of supersymmetric theories that have only boxes (and no triangles or bubbles at one-loop) and non-supersymmetric theories that are free of bubbles. In particular, our results indicate that one-loop scattering amplitudes in the N=2, SU(K) theory with a symmetric tensor hypermultiplet and an anti-symmetric tensor hypermultiplet are simple like those in the N=4 theory.