Conformal basis for flat space amplitudes

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: Global Translation Invariance Constraintsmentioning

confidence: 89%

Poincaré constraints on celestial amplitudes

Law

Zlotnikov

2020

“…This arose from the lack of a clear prescription for distributing counterterms in the conformal block expansion. Given the recent interest in using conformally covariant basis functions other than the traditional blocks, it is possible that results in [52][53][54][55][56] could help ensure that we are using the right language.…”

Section: Jhep03(2018)127 4 Conclusionmentioning

confidence: 99%

Conformal manifolds: ODEs from OPEs

Behan

2018

Abstract:The existence of an exactly marginal deformation in a conformal field theory is very special, but it is not well understood how this is reflected in the allowed dimensions and OPE coefficients of local operators. To shed light on this question, we compute perturbative corrections to several observables in an abstract CFT, starting with the beta function. This yields a sum rule that the theory must obey in order to be part of a conformal manifold. The set of constraints relating CFT data at different values of the coupling can in principle be written as a dynamical system that allows one to flow arbitrarily far. We begin the analysis of it by finding a simple form for the differential equations when the spacetime and theory space are both one-dimensional. A useful feature we can immediately observe is that our system makes it very difficult for level crossing to occur.

“…Here we have regularized the integral as described in section- (2). The σ i integrals are done by simply using the delta functions.…”

Section: Four Particle Graviton Tree Amplitude In Einstein Gravitymentioning

confidence: 99%

“…Therefore, from a holographic perspective, it is desirable to have a (complete) set of observables which transform naturally under the (Lorentz) conformal group. In order to achieve this [1][2][3] has put forward a very interesting proposal in which, instead of plane-waves, one uses the conformal primary wave-functions to describe the states of the incoming and outgoing particles in an S-matrix element. To be more precise, for massless particles, the change of basis is given by [1][2][3],S…”

Section: Introductionmentioning

confidence: 99%

Modified celestial amplitude in Einstein gravity

Banerjee

Ghosh

Pandey

et al. 2020

In this paper we evaluate the modified celestial amplitude for gravitons and gluons, as defined in arXiv:1801.10171 [hep-th]. We find that the modified (tree) amplitude is finite for gravitons in Einstein gravity. The modified amplitude behaves like correlation function of operators inserted at various points of null-infinity in the Minkowski space-time. Therefore, unlike the standard celestial amplitudes, these are three dimensional objects. We also show that this amplitude admits conformal soft factorization recently studied in the literature.