Classifying and constraining local four photon and four graviton S-matrices

Abstract

We study the space of all kinematically allowed four photon and four graviton S-matrices, polynomial in scattering momenta. We demonstrate that this space is the permutation invariant sector of a module over the ring of polynomials of the Mandelstam invariants s, t and u. We construct these modules for every value of the spacetime dimension D, and so explicitly count and parameterize the most general four photon and four graviton S-matrix at any given derivative order. We also explicitly list the local Lagrangians that give rise to these S-matrices. We then conjecture that the Regge growth of S-matrices in all physically acceptable classical theories is bounded by s 2 at fixed t. A four parameter subset of the polynomial photon S-matrices constructed above satisfies this Regge criterion. For gravitons, on the other hand, no polynomial addition to the Einstein S-matrix obeys this bound for D ≤ 6. For D ≥ 7 there is a single six derivative polynomial Lagrangian consistent with our conjectured Regge growth bound. Our conjecture thus implies that the Einstein four graviton S-matrix does not admit any physically acceptable polynomial modifications for D ≤ 6. A preliminary analysis also suggests that every finite sum of pole exchange contributions to four graviton scattering also violates our conjectured Regge growth bound, at least when D ≤ 6, even when the exchanged particles have low spin.

Causality of black holes in 4-dimensional Einstein–Gauss–Bonnet–Maxwell theory

“…Note that these results were obtained by following the procedure proposed in [13]: First define the Gauss-Bonnet coupling α → α D−4 and then take D → 4 limit. The results obtained here is comparable and consistent with the causality constraint on corrections to the graviton three-point coupling obtained in [48][49][50]. The contribution of this modified EGB term to the three-point function of gravitons deserves further studies.…”

“…The causality problem is closely related to the on-shell three-point functions of the weakly coupled gravity for the reason that the three-point functions determine the time delay. It was shown in [48] that in a theory with up to spin 2 particles the causality problem can only be solved when α 4 = 0, where α 4 is the coupling of the perturbations of the general form of the second order of the gravity: [49,50] for related discussions).…”

Classification of four-point local gluon S-matrices

“…S 4 invariant S-matrices, Z S-matrix = Tr x ∂ , (1.11) where ∂ is the overall momentum homogeneity. As argued in [1], local physical S-matrices are in one-to-one correspondence with the equivalence classes of quartic Lagrangians. The Lagrangians are said to be equivalent if their difference either vanishes on-shell or is a total derivative.…”

“…The n-point gluon scattering amplitude is a function S( µ . 1 Here µ and a is the Lorentz and G-adjoint color index respectively. The superscript (i) labels each gluon and goes from 1, .…”

Four-point functions in large N Chern-Simons fermionic theories

“…However, we believe that this is an artefact of the collinear regime, and do not know if it holds in the general case. 8 We thank S. Minwalla for this information, based on [20].…”