Gluon amplitudes as 2d conformal correlators

Abstract

Recently, spin-one wavefunctions in four dimensions that are conformal primaries of the Lorentz group SL(2, C) were constructed. We compute low-point, tree-level gluon scattering amplitudes in the space of these conformal primary wavefunctions. The answers have the same conformal covariance as correlators of spin-one primaries in a 2d CFT. The BCFW recursion relation between three-and four-point gluon amplitudes is recast into this conformal basis.

Poincaré constraints on celestial amplitudes

“…Permuting particle indices produces alternative three-point structure parametrizations that are equally valid. 7 Once again, we emphasize that this symmetry relation was first found by Strominger et al with regard to OPE coefficients and, in essence, was made public by Strominger in the talk [29] earlier this year. Our independent calculation agrees with their finding.…”

“…As in [7], we consider the A −−+ 3 = ⟨12⟩ 3 (⟨23⟩⟨31⟩) three-point gluon amplitude with particles 1, 2 incoming and 3 outgoing; where spinor helicity brackets are resolved as…”

“…As a next step, we proceed to solve the equations ∑ j j P µ j A 4 = 0 to find further constraints on f h 1 ,h 2 ,h 3 ,h 4 h 1 ,h 2 ,h 3 ,h 4 (z,z). We recall the following cross ratio regions for different incoming and outgoing particle configurations, which always arise in massless 4-pt celestial amplitudes due to the presence of total momentum conservation delta functions in Minkowski space amplitudes regardless of any other amplitude features (see, e.g., example in [7]):…”

“…where now we abbreviate ∆ 1 = ∆, ∆ 2 = 1 + ∆. It is clear that both resulting vanishing conditions can be reconciled only if we demand 7) in which case the constraint is solved by…”

BMS symmetry of celestial OPE

“…Celestial CFT is conjectured to be the holographic dual of quantum gravity in asymptotically flat space-time [4][5][6][7][8]. The observables of the celestial CFT are related to Mellin transformations of flat space scattering amplitudes [19][20][21][22][23][24][25][26]. Under Lorentz transformations, which act on the celestial sphere as global conformal group, Mellin amplitudes transform like correlation functions of a CFT.…”