Group-theoretic relations for amplitudes in gauge theories with orthogonal and symplectic groups

Abstract

It is important to find nontrivial constraint relations for color-ordered amplitudes in gauge theories. In the past several years, a pure group-theoretic iterative method has been proposed to derive linear constraints on color-ordered amplitudes in SU(N) gauge theories. In this paper, we use the same method to derive linear constraints on four-point gluon amplitudes in SO(N) and Sp(2N) gauge theories. These constraints are derived up to four-loop order. It is found that there are $n=1,6,10,13,16$ constraint relations at $L=0,1,2,3,4$ loop orders in both SO(N) and Sp(2N) cases. Correspondingly, the numbers of independent four-point color-ordered amplitudes are $2,3,5,8,11$ at $L=0,1,2,3,4$ loop orders in both theories.

23 pages,text partially overlap with arXiv:1511.09333

References in corpus (5)

• 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

Cited by in corpus (1)

• Strong coupling expansion of free energy and BPS Wilson loop in $\mathcal{N}=2$ superconformal models with fundamental hypermultiplets