Conformal Blocks from Celestial Gluon Amplitudes II: Single-valued Correlators

Abstract

In a recent paper, here referred to as part I, we considered the celestial four-gluon amplitude with one gluon represented by the shadow transform of the corresponding primary field operator. This correlator is ill-defined because it contains branch points related to the presence of conformal blocks with complex spin. In this work, we adopt a procedure similar to minimal models and construct a single-valued completion of the shadow correlator, in the limit when the shadow is "soft." By following the approach of Dotsenko and Fateev, we obtain an integral representation of such a single-valued correlator. This allows inverting the shadow transform and constructing a single-valued celestial four-gluon amplitude. This amplitude is drastically different from the original Mellin amplitude. It is defined over the entire complex plane and has correct crossing symmetry, OPE and bootstrap properties. It agrees with all known OPEs of celestial gluon operators. The conformal block spectrum consists of primary fields with dimensions $\Delta =m+i\lambda$, with integer $m\ge 1$ and various, but always integer spin, in all group representations contained in the product of two adjoint representations.

35 pages

References in corpus (10)

• Lectures on Celestial Amplitudes
• Gluon Amplitudes as 2d Conformal Correlators
• Symmetries of Celestial Amplitudes
• Conformal Block Expansion in Celestial CFT
• Conformal Blocks from Celestial Gluon Amplitudes
• Lectures on Celestial Holography
• State-Operator Correspondence in Celestial Conformal Field Theory
• Ambidextrous light transforms for celestial amplitudes
• Celestial Dual Superconformal Symmetry, MHV Amplitudes and Differential Equations
• Coaction and double-copy properties of configuration-space integrals at genus zero

Cited by in corpus (18)

• Bridging Carrollian and Celestial Holography
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Celestial operator products from the worldsheet
• Elements of Celestial Conformal Field Theory
• Celestial Liouville Theory for Yang-Mills Amplitudes
• Four-point correlators of light-ray operators in CCFT
• Celestial Locality and the Jacobi Identity
• All-order celestial OPE in the MHV sector
• Celestial Yang-Mills Amplitudes and D=4 Conformal Blocks
• Shadow Celestial Amplitude
• Notes on Resonances and Unitarity from Celestial Amplitudes
• Celestial Recursion
• Celestial amplitudes in an ambidextrous basis
• Celestial Geometry
• All-order celestial OPE from on-shell recursion
• Integrable Field Theories and Their CCFT Duals
• Light transformed gluon correlators in CCFT
• Celestial Regge theory