Covariant Propagators and Vertices for Higher Spin Bosons

171

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.

Section: Jhep02(2020)114mentioning

confidence: 99%

Section: Jhep02(2020)114mentioning

confidence: 99%

See 1 more Smart Citation

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

Chowdhury

Gadde

Gopalka

et al. 2020

171

“…If the vector particle is massless (photon) then we have gauge invariance 5) which leads to the constraint…”

Section: Scattering Amplitudes For Spinning Particlesmentioning

confidence: 99%

“…Following Mack [1,2], we shall argue that this factorization is best formulated in Mellin space. Consider the Mellin amplitude associated with a n-point function of scalar primary operators O i of dimension ∆ i , 1 4) where the integration [dγ] is subject to the constraints 2 5) ensuring that the correlation function transforms appropriately under conformal transformations. The integration contours for the independent γ ij variables run parallel to the imaginary axis.…”

Section: Introductionmentioning

confidence: 99%

Factorization of Mellin amplitudes

Gonçalves

Penedones

Trevisani

2015

146

We introduce Mellin amplitudes for correlation functions of k scalar operators and one operator with spin in conformal field theories (CFT) in general dimension. We show that Mellin amplitudes for scalar operators have simple poles with residues that factorize in terms of lower point Mellin amplitudes, similarly to what happens for scattering amplitudes in flat space. Finally, we study the flat space limit of Anti-de Sitter (AdS) space, in the context of the AdS/CFT correspondence, and generalize a formula relating CFT Mellin amplitudes to scattering amplitudes of the bulk theory, including particles with spin.

Spinning amplitudes from scalar amplitudes

Balasubramanian

Patil

Rudra

2021

We provide a systematic method to compute tree-level scattering amplitudes with spinning external states from amplitudes with scalar external states in arbitrary spacetime dimensions. We write down analytic answers for various scattering amplitudes, including the four graviton amplitude due to the massive spin J exchange. We verify the results by computing angular distributions in 3 + 1 dimensions using various identities involving Jacobi polynomials.