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

TL;DR

This paper extends a group-theoretic approach to study linear relations among color-ordered gluon amplitudes in orthogonal gauge theories, revealing specific constraints at various loop levels and highlighting differences from the special unitary case.

Contribution

It applies a pure group-theoretic method to orthogonal gauge theories, identifying new loop-level amplitude relations and constraints.

Findings

Identifies 1,6,10,13,16 constraints at loop levels 0-4 in SO(N) gauge theories.

Shows more constraints are expected at higher loop levels.

Highlights differences from SU(N) gauge theories where constraints are fewer at high loops.

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 $(L\geqslant 2)$ loop amplitudes.