Jul 18 – 23, 2022
University of Vienna
Europe/Vienna timezone

Celestial Operator Product Expansions and ${\rm w}_{1+\infty}$ Symmetry

Not scheduled
Audimax (University of Vienna)


University of Vienna

Universitätsring 1, 1010 Vienna, Austria
Gong Show Talk Gong Show


Elizabeth Himwich


The Lorentz symmetry of four-dimensional (4D) scattering is isomorphic to two-dimensional (2D) global conformal symmetry. As a consequence, amplitudes in 4D momentum space can be naturally recast via a Mellin transform as correlation functions of 2D ''celestial'' conformal primary operators. In this talk, I will describe results (with M. Pate and K. Singh) on operator product expansions of massless celestial primary operators with arbitrary spin and arbitrary 4D three-point couplings. For such operators, Poincare symmetry implies 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 precisely match those derived from momentum-space tree-level collinear limits, and they respect an infinite number of additional constraints associated with an underlying ${\rm w_{1+\infty}}$ algebra. I will also comment on ongoing work (with M. Pate) to generalize the ${\rm w}_{1+\infty}$ symmetry action to massive amplitudes.

Primary author


Kyle Singh (University of Pennsylvania) Monica Pate (Harvard University)

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