Rational Terms in Theories with Matter

TL;DR

This paper investigates rational remainders in gluon amplitudes within gauge theories coupled to matter, revealing their dependence on specific invariants and identifying classes of theories where these remainders vanish, challenging naive power counting expectations.

Contribution

It introduces a classification of rational remainders based on matter representation invariants and identifies non-supersymmetric theories with vanishing rational remainders.

Findings

Rational remainders depend only on second and fourth order indices.

Identifies an infinite class of theories with vanishing rational remainders.

Provides examples where rational remainders vanish despite naive expectations.

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.