Group-theoretic relations for partial amplitudes in gauge theories with orthogonal group

Abstract

It is very important to find some nontrivial relations for color-ordered amplitudes at loop levels. In the last several years, a pure group-theoretic method has been proposed to study loop level relations for color-ordered amplitudes in $\sun$ gauge theories. In this paper, we apply the same method to study the linear relations for loop level four point color-ordered gluon amplitudes in gauge theory with $\son$ group and find that there are $1,6,10,13,16$ constraint relations at $L=0,1,2,3,4$ loop level. It is expected that there are more group-theoretic constraints for high loop levels. The constraint relations should be derived order by order in $\son$ gauge theories. This is unlike the $\sun$ case, where there are only four constraints for higher $(L⩾2)$ loop amplitudes.

mistakes corrected, conclusion changed

References in corpus (6)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
• Realistic three-generation models from SO(32) heterotic string theory

Cited by in corpus (2)

• Group constraint relations for five-point amplitudes in gauge theories with SO(N) and Sp(2N) groups
• Strong coupling expansion of free energy and BPS Wilson loop in $\mathcal{N}=2$ superconformal models with fundamental hypermultiplets