Deforming Soft Algebras for Gauge Theory

Abstract

Symmetry algebras deriving from towers of soft theorems can be deformed by a short list of higher-dimension Wilsonian corrections to the effective action. We study the simplest of these deformations in gauge theory arising from a massless complex scalar coupled to $F^2$. The soft gauge symmetry '$s$-algebra', compactly realized as a higher-spin current algebra acting on the celestial sphere, is deformed and enlarged to an associative algebra containing soft scalar generators. This deformed soft algebra is found to be non-abelian even in abelian gauge theory. A two-parameter family of central extensions of the $s$-subalgebra are generated by shifting and decoupling the scalar generators. It is shown that these central extensions can also be generated by expanding around a certain non-trivial but Lorentz invariant shockwave type background for the scalar field.

arXiv comment13 pages, 1 figure

References in corpus (19)

• Asymptotic Symmetries of Yang-Mills Theory
• MHV Rules for Higgs Plus Multi-Gluon Amplitudes
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• 2D Kac-Moody Symmetry of 4D Yang-Mills Theory
• Conformally Soft Theorem in Gauge Theory
• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• Celestial holography meets twisted holography: 4d amplitudes from chiral correlators
• Soft Photon and Graviton Theorems in Effective Field Theory
• $(2,2)$ Scattering and the Celestial Torus
• Top-down holography in an asymptotically flat spacetime
• Celestial Amplitudes as AdS-Witten Diagrams
• On Effective Field Theories with Celestial Duals
• Elements of Celestial Conformal Field Theory
• Celestial holography on Kerr-Schild backgrounds
• Celestial Liouville Theory for Yang-Mills Amplitudes
• Soft Scalars and the Geometry of the Space of Celestial CFTs
• On the associativity of 1-loop corrections to the celestial operator product in gravity
• Celestial Locality and the Jacobi Identity
• Celestial Yang-Mills Amplitudes and D=4 Conformal Blocks

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• Celestial $s{w}_{1+\infty }$ algebra in Einstein-Yang-Mills theory
• Asymptotic Higher Spin Symmetries III: Noether Realization in Yang-Mills Theory
• Entanglement Rényi entropies in celestial holography
• Loop corrections versus marginal deformation in celestial holography