Celestial Liouville Theory for Yang-Mills Amplitudes

Abstract

We consider Yang-Mills theory with the coupling constant and theta angle determined by the vacuum expectation values of a dynamical (complex) dilaton field. We discuss the tree-level N-gluon MHV scattering amplitudes in the presence of a nontrivial background dilaton field and construct the corresponding celestial amplitudes by taking Mellin transforms with respect to the lightcone energies. In this way, we obtain two-dimensional CFT correlators of primary fields on the celestial sphere. We show that the celestial Yang-Mills amplitudes evaluated in the presence of a spherical dilaton shockwave are given by the correlation functions of primary field operators factorized into the holomorphic current operators times the "light" Liouville operators. They are evaluated in the semiclassical limit of Liouville theory (the limit of infinite central charge) and are determined by the classical Liouville field describing metrics on the celestial sphere.

arXiv comment12 pages

References in corpus (15)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Conformal Four Point Functions and the Operator Product Expansion
• Conformal Partial Waves and the Operator Product Expansion
• Two and three-point functions in Liouville theory
• Projectors, Shadows, and Conformal Blocks
• A Conformal Basis for Flat Space Amplitudes
• Lectures on Celestial Amplitudes
• MHV Rules for Higgs Plus Multi-Gluon Amplitudes
• Gluon Amplitudes as 2d Conformal Correlators
• Conformal Blocks from Celestial Gluon Amplitudes
• Elements of Celestial Conformal Field Theory
• Celestial Dual Superconformal Symmetry, MHV Amplitudes and Differential Equations
• Conformal Blocks from Celestial Gluon Amplitudes II: Single-valued Correlators
• A Course in Amplitudes

Cited by in corpus (12)

• Deforming Soft Algebras for Gauge Theory
• Carrollian conformal scalar as flat-space singleton
• Celestial Leaf Amplitudes
• Towards higher-spin holography in flat space
• Celestial Supersymmetry
• Chiral higher-spin holography in flat space: the Flato-Fronsdal theorem and lower-point functions
• Lorentz Symmetry and IR Structure of The BFSS Matrix Model
• Integrable Field Theories and Their CCFT Duals
• Celestial self-dual Yang-Mills theory: a new formula and the OPE limit
• Spectral representation in Klein space: simplifying celestial leaf amplitudes
• Celestial Gluon Amplitudes from the Outside In
• Entanglement Rényi entropies in celestial holography