Modified celestial amplitude in Einstein gravity

The functional structure of celestial amplitudes as constrained by Poincaré symmetry is investigated in 2, 3, and 4-point cases for massless external particles of various spin, as well as massive external scalars. Functional constraints and recurrence relations are found (akin to the findings in 1901.01622) that must be obeyed by the respective permissible correlator structures and function coefficients. In specific three-point cases involving massive scalars the resulting recurrence relations can be solved, e.g., reproducing purely from symmetry a three-point function coefficient known in the literature. Additionally, as a byproduct of the analysis, the three-point function coefficient for gluons in Minkowski signature is obtained from an amplitude map to the celestial sphere.

Section: Introductionmentioning

confidence: 99%

Poincaré constraints on celestial amplitudes

Law

Zlotnikov

2020

“…Similarly, the Mellin integral of the second term in eq. (B.2) is g(λ 1 )g(λ 6 )g(λ 7 ) ∞ 0 dω 1 dω 6 dω 7 ω iλ 1 1 ω iλ 6 6 ω iλ 7…”

Section: Jhep09(2020)139mentioning

confidence: 99%

“…Indeed, scattering amplitudes in D = 4 Minkowski spacetime can be recast, via a Mellin transform, into conformal correlation functions (celestial amplitudes) on the celestial sphere [1][2][3][4][5][6]. 1 The theory describing the dynamics of celestial amplitudes is expected to be a novel conformal field theory on CS 2 .…”

Section: Introductionmentioning

confidence: 99%

On Sugawara construction on celestial sphere

Fan

Fotopoulos

Stieberger

et al. 2020

Conformally soft gluons are conserved currents of the Celestial Conformal Field Theory (CCFT) and generate a Kac-Moody algebra. We study celestial amplitudes of Yang-Mills theory, which are Mellin transforms of gluon amplitudes and take the double soft limit of a pair of gluons. In this manner we construct the Sugawara energy-momentum tensor of the CCFT. We verify that conformally soft gauge bosons are Virasoro primaries of the CCFT under the Sugawara energy-momentum tensor. The Sugawara tensor though does not generate the correct conformal transformations for hard states. In Einstein-Yang- Mills theory, we consider an alternative construction of the energy-momentum tensor, similar to the double copy construction which relates gauge theory amplitudes with gravity ones. This energy momentum tensor has the correct properties to generate conformal transformations for both soft and hard states. We extend this construction to supertranslations.

“…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.…”

Section: Introductionmentioning

confidence: 99%

BMS symmetry of celestial OPE

Banerjee

Ghosh

Gonzo

2020

Self Cite

106

103

In this paper we study the BMS symmetry of the celestial OPE of two positive helicity gravitons in Einstein theory in four dimensions. The celestial OPE is obtained by Mellin transforming the scattering amplitude in the (holomorphic) collinear limit. The collinear limit at leading order gives the singular term of the celestial OPE. We compute the first subleading correction to the OPE by analysing the four graviton scattering amplitude directly in Mellin space. The subleading term can be written as a linear combination of BMS descendants with the OPE coefficients determined by BMS algebra and the coefficient of the leading term in the OPE. This can be done by defining a suitable BMS primary state. We find that among the descendants, which appear at the first subleading order, there is one which is created by holomorphic supertranslation with simple pole on the celestial sphere.