Classification of four-point local gluon S-matrices

Abstract

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.

Bounds on Regge growth of flat space scattering from bounds on chaos

“…For instance, all two derivative classical theories always obey the CRG conjecture [2]. Moreover, the classical Einstein S matrix saturates CRG growth 4 and the Type II and Heterotic analogues of the Virasoro Shapiro amplitude of string theory temper this growth to a power that is strictly less than two at every physical finite value of α t (see [2] for some more details).…”

“…That is a causal classical theory whose energy is bounded from below (and perhaps is also required to obey other constraints of a similar general nature). See[2,3] for a discussion and[4] for a generalization to gluons.…”

Bulk locality for scalars and fermions with global symmetry

“…In order to evaluate the bulk contact interaction, we follow the techniques of [17,18] to group theoretically evaluate the "local module" for the four point scalar and fermions charged under global symmetry. As defined in [17], local modules are in one-to-one correspondence with local bulk Lagrangians and are graded by order of derivatives and S 3 transformation properties (S 2 for D = 2 fermion S-matrices).…”

“…In this section we follow [17,18] to evaluate flat space S-matrices for scalars in D ≥ 4 and determine the number of bulk contact terms with finite support over spin. Local Lagrangians are isomorphic to flat space s-matrices upto field re-definitions and equations of motion.…”

“…where dµ SO(D) is the Haar measure associated with the Lorentz group SO(D) and dµ G is the Haar measure associated with the colour group G. Using techniques outlined in appendix C of [18] and appendix H.1 of [17], the Haar integral over the SO(D) can be performed and (2.52) then takes the schematic form,…”