Scattering off of Twistorial Line Defects

TL;DR

This work extends the celestial chiral algebra bootstrap to 4d twistorial theories in the presence of twistorial line defects, realized as self-dual dyons, by leveraging non-Hausdorff twistor spaces and relative cohomology. Central tools include holomorphic BF theory on $ ext{PT}_Q$, the Coulomb bundle background, and Koszul duality, which together yield a differential-graded celestial symmetry algebra encoding defect data. The authors explicitly reproduce the $n$-point tree-level $MHV$ gluon amplitudes in backgrounds with a self-dual dyon (ABMS1/ABMS2) and derive the corresponding defect-modified conformal blocks, as well as provide a systematic framework to lift 4d operators like $ ext{Tr}(B^2)$ to $ ext{PT}_Q$ to obtain form factors and scattering amplitudes in the presence of the defect. This establishes an algebraic, defect-respecting path to all-multiplicity scattering in twistorial backgrounds, with potential extensions to loop levels and more general backgrounds in celestial holography.

Abstract

The recently devised chiral algebra bootstrap computes the form factors of a special class of ``twistorial'' 4d QFTs as correlation functions of the theory's 2d celestial chiral algebra. Examples of twistorial theories include self-dual Yang-Mills theory coupled to special massless matter content, and certain form factors in these theories are equivalent to a subset of MHV amplitudes in massless QCD, coupled to the same matter. In this paper, we extend the chiral algebra bootstrap to include scattering in the presence of charged sources, using a self-dual dyon in a twistorial theory as our main example. Self-dual theories in the presence of such sources lift to holomorphic gauge theories on non-Hausdorff twistor space, and we generalize the Koszul duality construction of Costello and Paquette to this setting. With this approach, we easily reproduce a recent formula of Adamo, Bogna, Mason, and Sharma for $n$-point MHV scattering of gluons off the self-dual dyon.