Abstract
We study rational remainders associated with gluon amplitudes in gauge theories coupled to matter in arbitrary representations. We find that these terms depend on only a small number of invariants of the matter-representation called indices. In particular, rational remainders can depend on the second and fourth order indices only. Using this, we find an infinite class of non-supersymmetric theories in which rational remainders vanish for gluon amplitudes. This class includes all the "next-to-simplest" quantum field theories of arXiv:0910.0930. This provides new examples of amplitudes in which rational remainders vanish even though naive power counting would suggest their presence.
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