On Sugawara construction on Celestial Sphere

Abstract

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 (EYM) 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.

39 pages

References in corpus (9)

• New Relations for Gauge-Theory Amplitudes
• Gluon Amplitudes as 2d Conformal Correlators
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Symmetries of Celestial Amplitudes
• Hard-Soft-Collinear Factorization to All Orders
• BMS Symmetry of Celestial OPE
• Extended Super BMS Algebra of Celestial CFT
• Soft Limits of Yang-Mills Amplitudes and Conformal Correlators
• Massive Spinning Bosons on the Celestial Sphere

Cited by in corpus (19)

• Lectures on Celestial Amplitudes
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Bridging Carrollian and Celestial Holography
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Double Copy for Celestial Amplitudes
• Shifting Spin on the Celestial Sphere
• Revisiting the Conformally Soft Sector with Celestial Diamonds
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• Loops on the Celestial Sphere
• Holographic Chiral Algebra: Supersymmetry, Infinite Ward Identities, and EFTs
• Coadjoint representation of the BMS group on celestial Riemann surfaces
• Ambidextrous light transforms for celestial amplitudes
• Celestial double copy from the worldsheet
• Relativistic partial waves for celestial amplitudes
• Descendants in celestial CFT and emergent multi-collinear factorization
• From Celestial Correlators to AdS, and back
• The structure of IR divergences in celestial gluon amplitudes
• Asymptotic symmetries in spatially flat FRW
• Celestial IR divergences and the effective action of supertranslation modes