Conformal block expansion in celestial CFT

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: Scalarssupporting

confidence: 90%

Section: Light Transformmentioning

confidence: 99%

Section: Scalarsmentioning

confidence: 99%

“…To be general, we will work with the latter case. Following [15], one tames this integral using a regulator that partially breaks conformal covariance. Consider the regulated definition…”

Section: Scalarsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Ambidextrous light transforms for celestial amplitudes

Sharma

2022

Celestial operator product expansions and w1+∞ symmetry for all spins

Himwich

Pate

Singh

2022

The operator product expansion of massless celestial primary operators of arbitrary spin is investigated. Poincaré symmetry is found to imply a set of recursion relations on the operator product expansion coefficients of the leading singular terms at tree-level in a holomorphic limit. The symmetry constraints are solved by an Euler beta function with arguments that depend simply on the right-moving conformal weights of the operators in the product. These symmetry-derived coefficients are shown not only to match precisely those arising from momentum-space tree-level collinear limits, but also to obey an infinite number of additional symmetry transformations that respect the algebra of w1+∞. In tree-level minimally-coupled gravitational theories, celestial currents are constructed from light transforms of conformally soft gravitons and found to generate the action of w1+∞ on arbitrary massless celestial primaries. Results include operator product expansion coefficients for fermions as well as those arising from higher-derivative non-minimal couplings of gluons and gravitons.

Light transformed gluon correlators in CCFT

Banerjee

Basu

Bhatkar

2023

In the present work, we study celestial correlators of light transformed gluon operators at tree level. We also discuss the transformation of light transformed operators under the action of 4D translations. The two, three and four-point functions arising from MHV amplitudes in terms of light transformed operators satisfy translation invariance constraints, are non-distributional and contain ordinary CFT power law terms. There is a new channel dependent term in the three point function. We show that the three-point light transformed correlation function is conformally covariant after contributions from all the three channels are added. We also study the OPE limit of the different channels of the three-point function in an attempt to construct a map between the OPE in the Mellin basis and that in the light transformed one.