Loops on the Celestial Sphere

Abstract

We study the effect of loop corrections to conformal correlators on the celestial sphere at null infinity. We first analyze finite one-loop celestial amplitudes in pure Yang-Mills theory and Einstein gravity. We then turn to our main focus: infrared divergent loop amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory. We compute the celestial one-loop amplitude in dimensional regularization and show that it can be recast as an operator acting on the celestial tree-level amplitude. This extends to any loop order and the re-summation of all planar loops enables us to write down an expression for the all-loop celestial amplitude. Finally, we show that the exponentiated all-loop expression given by the BDS formula gets promoted on the celestial sphere to an operator acting on the tree-level conformal correlation function, thus yielding, the celestial BDS formula.

18 pages. Version 2: typos corrected, comments added

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Cited by in corpus (32)

• Lectures on Celestial Amplitudes
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Celestial Amplitudes from UV to IR
• Celestial Diamonds: Conformal Multiplets in Celestial CFT
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Conformal Block Expansion in Celestial CFT
• Shifting Spin on the Celestial Sphere
• Revisiting the Conformally Soft Sector with Celestial Diamonds
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• Charge Algebra in Al(A)dS${}_n$ Spacetimes
• Lectures on Celestial Holography
• Coadjoint representation of the BMS group on celestial Riemann surfaces
• Celestial double copy from the worldsheet
• Non-abelian infrared divergences on the celestial sphere
• Celestial Dual Superconformal Symmetry, MHV Amplitudes and Differential Equations
• Loop-level gluon OPEs in celestial holography
• Subsubleading soft graviton symmetry and MHV graviton scattering amplitudes
• Celestial superamplitude in $\mathcal{N}=4$ SYM theory
• The structure of IR divergences in celestial gluon amplitudes
• Celestial Superamplitudes
• (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes
• Integrable Field Theories and Their CCFT Duals
• The Grassmannian for Celestial Superamplitudes
• Celestial IR divergences in general most-subleading-color gluon and gravity amplitudes
• Zwanziger's pairwise little group on the celestial sphere
• The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity
• Loop corrections versus marginal deformation in celestial holography
• Charge algebra for non-abelian large gauge symmetries at $O(r)$
• Celestial Eikonal Amplitudes in the Near-Horizon Region
• Celestial Holography
• Non-abelian soft radiation data for a celestial theory
• Perturbatively Exact $w_{1+\infty }$ Asymptotic Symmetry of Quantum Self-Dual Gravity