Classification of four-point local gluon S-matrices

• Published in: The journal of high energy physics Vol. 2021; no. 1; pp. 1 - 41
• Main Authors: Chowdhury, Subham Dutta, Gadde, Abhijit
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2021; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Classification; Effective Field Theories; Elementary Particles; Field Theories in Higher Dimensions; Gluons; Gravitons; Group theory; High energy physics; Lie groups; Mathematical analysis; Matrix methods; Permutations; Photons; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; S matrix theory; Scalars; Scattering Amplitudes; String Theory; Effective Field Theories; Scattering Amplitudes; Field Theories in Higher Dimensions
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP01(2021)104

A bstract In this paper, we classify four-point local gluon S-matrices in arbitrary dimensions. This is along the same lines as [1] where four-point local photon S-matrices and graviton S-matrices were classified. We do the classification explicitly for gauge groups SO( N ) and SU( N ) for all N but our method is easily generalizable to other Lie groups. The construction involves combining not-necessarily-permutation-symmetric four-point S-matrices of photons and those of adjoint scalars into permutation symmetric four-point gluon S-matrix. We explicitly list both the components of the construction, i.e permutation symmetric as well as non-symmetric four point S-matrices, for both the photons as well as the adjoint scalars for arbitrary dimensions and for gauge groups SO( N ) and SU( N ) for all N . In this paper, we explicitly list the local Lagrangians that generate the local gluon S-matrices for D ≥ 9 and present the relevant counting for lower dimensions. Local Lagrangians for gluon S-matrices in lower dimensions can be written down following the same method. We also express the Yang-Mills four gluon S-matrix with gluon exchange in terms of our basis structures.