Celestial Recursion

TL;DR

This paper explores BCFW recursion relations in celestial amplitudes, linking them to asymptotic symmetries and the celestial bootstrap, and extends the framework to super-BCFW, highlighting key limits and open questions.

Contribution

It recasts celestial BCFW shifts as symmetry actions, analyzes their limits, and connects them to celestial bootstrap constraints, including an extension to super-BCFW.

Findings

Large-$z$ behavior determines allowed shifts

Infinitesimal limit relates to celestial bootstrap constraints

Extension to super-BCFW broadens the framework

Abstract

We examine the BCFW recursion relations for celestial amplitudes and how they inform the celestial bootstrap program. We start by recasting the celestial incarnation of the BCFW shift as a generalization of the action of familiar asymptotic symmetries on hard particles, before focusing on two limits: $z\to \infty$ and $z\to 0$. We then discuss how the celestial CFT data encodes the large-$z$ behavior determining which shifts are allowed, while the infinitesimal limit is tied to the celestial bootstrap program via the BG equations that constrain the MHV sector. The extension to super-BCFW is also presented. We close by remarking on several open questions for future study.