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The Next-to-Simplest Quantum Field Theories
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.Comment: 53 pages; (v2) reference to gravity dual and subsection on large N
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