(2, 2) Scattering and the celestial torus

Low multiplicity celestial amplitudes of gluons and gravitons tend to be distributional in the celestial coordinates z,$$ \overline{z} $$ z ¯ . We provide a new systematic remedy to this situation by studying celestial amplitudes in a basis of light transformed boost eigenstates. Motivated by a novel equivalence between light transforms and Witten’s half-Fourier transforms to twistor space, we light transform every positive helicity state in the coordinate z and every negative helicity state in $$ \overline{z} $$ z ¯ . With examples, we show that this “ambidextrous” prescription beautifully recasts two- and three-point celestial amplitudes in terms of standard conformally covariant structures. These are used to extract examples of celestial OPE for light transformed operators. We also study such amplitudes at higher multiplicity by constructing the Grassmannian representation of tree-level gluon celestial amplitudes as well as their light transforms. The formulae for n-point Nk−2MHV amplitudes take the form of Euler-type integrals over regions in Gr(k, n) cut out by positive energy constraints.

Section: Preliminariesmentioning

confidence: 99%

“…In this work, we wish to focus on a refinement of the shadow transform in Lorentzian signature, namely the light transform. The authors of [14] studied CCFT on the celestial torus of flat space R 2,2 with a split signature metric. This is a Lorentzian CFT and hence contains light ray operators with analytically continued spins [2].…”

Section: Introductionmentioning

confidence: 99%

Ambidextrous light transforms for celestial amplitudes

Sharma

2022

“…3 Throughout this paper we treat left and right movers as independent on the celestial sphere, which means we effectively work in (2, 2) signature, i.e. Klein space [62]. The SL(2, R)R here is the global subgroup of the VirR superrotations.…”

Section: Introductionmentioning

confidence: 99%

“…Recall we are working with independent left and right coordinates, i.e. (2, 2) signature[62] 15. To make connection with the standard four-point KLT formula as described in[74,75], it is convenient to set z1 = 1, z2 = 0 using SL(2, R) covariance and expand O (h P , hP ) (z3, z3) in powers of z3, z3.…”

mentioning

confidence: 99%

Holographic symmetry algebras for gauge theory and gravity

Guevara

Himwich²,

Pate

et al. 2021

167

195

All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D currents acting on the celestial sphere. A complete classification of these symmetries and their algebras is an open problem. Here we construct two towers of such 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights. These generate the symmetries associated to an infinite tower of conformally soft theorems. The current algebra commutators are explicitly derived from the poles in the OPE coefficients, and found to comprise a rich closed subalgebra of the complete symmetry algebra.

“…They do not however form representations of the Poincaré group. Another basis of interest[21] which do furnish Poincaré representations, and moreover include the soft currents[22] are those with real integral ∆. In this paper we assume that ∆ lies on the unitary principal series but many of our formulae can be generalized to the integral case.…”

mentioning

confidence: 99%

State-operator correspondence in celestial conformal field theory

Crawley¹,

Miller²,

Narayanan³

et al. 2021

Self Cite

The bulk-to-boundary dictionary for 4D celestial holography is given a new entry defining 2D boundary states living on oriented circles on the celestial sphere. The states are constructed using the 2D CFT state-operator correspondence from operator insertions corresponding to either incoming or outgoing particles which cross the celestial sphere inside the circle. The BPZ construction is applied to give an inner product on such states whose associated bulk adjoints are shown to involve a shadow transform. Scattering amplitudes are then given by BPZ inner products between states living on the same circle but with opposite orientations. 2D boundary states are found to encode the same information as their 4D bulk counterparts, but organized in a radically different manner.