All-loop group-theory constraints for color-ordered SU(N) gauge-theory amplitudes
Stephen G. Naculich
TL;DR
This paper derives all-loop order constraints on color-ordered four-point amplitudes in SU(N) gauge theories based solely on gauge group structure, extending known relations like U(1) decoupling to higher loops.
Contribution
It introduces a general framework for all-loop group-theory constraints on gauge-theory amplitudes, expanding the understanding of gauge invariance at multiple loop levels.
Findings
Derived all-loop group-theory constraints for four-point amplitudes
Extended U(1) decoupling identities to all loop orders
Provided a systematic approach for analyzing gauge group structure effects
Abstract
We derive constraints on the color-ordered amplitudes of the L-loop four-point function in SU(N) gauge theories that arise solely from the structure of the gauge group. These constraints generalize well-known group theory relations, such as U(1) decoupling identities, to all loop orders.
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