The Next-to-Simplest Quantum Field Theories

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.

53 pages; (v2) reference to gravity dual and subsection on large N added

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• Four Point Functions of the Stress Tensor and Conserved Currents in AdS_4/CFT_3
• Wilson Loops in N=2 Superconformal Yang-Mills Theory
• Causality, Unitarity and Symmetry in Effective Field Theory
• Amplitudes for Multiple M5 Branes
• On-shell supersymmetry for massive multiplets
• One-loop renormalization and the S-matrix
• $\mathcal{N}=7$ On-Shell Diagrams and Supergravity Amplitudes in Momentum Twistor Space
• Scattering Amplitudes and BCFW in $\mathcal{N}=2^{\ast }$ Theory
• On the non-planar beta-deformed N=4 super-Yang-Mills theory
• Loop Amplitudes in the Coulomb Branch of $\mathcal{N}=4$ Super-Yang-Mills Theory
• Scattering amplitudes in gauge theories with and without supersymmetry
• Supersums for all supersymmetric amplitudes
• Bilocal phase operators in beta-deformed super Yang-Mills