Comments on Minitwistors and the Celestial Supersphere

TL;DR

This paper extends the RSVW formalism to celestial amplitudes, reformulating MHV amplitudes in terms of minitwistor wavefunctions and proposing supersymmetric celestial CFTs as sigma-models with concrete amplitude reproductions.

Contribution

It introduces a minitwistor formalism for celestial amplitudes and constructs supersymmetric celestial CFTs as sigma-models, linking string theory, twistor theory, and celestial holography.

Findings

Reformulation of MHV celestial amplitudes using minitwistor wavefunctions.

Construction of a minitwistor generating functional for MHV amplitudes.

Proposal of supersymmetric celestial CFTs as sigma-models reproducing known amplitudes.

Abstract

Continuing our program of deriving aspects of celestial holography from string theory, we extend the Roiban-Spradlin-Volovich-Witten (RSVW) formalism to celestial amplitudes. We reformulate the tree-level maximally-helicity-violating (MHV) celestial leaf amplitudes for gluons in $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) theory and for gravitons in $\mathcal{N}=8$ Supergravity in terms of minitwistor wavefunctions. These are defined as representatives of cohomology classes on the minitwistor space $\mathbf{MT}$, associated to the three-dimensional Euclidean anti-de Sitter space. In this framework, celestial leaf amplitudes are expressed as integrals over the moduli space of minitwistor lines. We construct a minitwistor generating functional for MHV leaf amplitudes using the Quillen determinant line bundle, extending the approach originally developed by Boels, Mason and Skinner. Building on this formalism, we propose supersymmetric celestial conformal field theories (CFTs) as $\sigma$-models, where the worldsheet is given by the celestial supersphere $\mathbf{CP}^{1|2}$, and the target space is the minitwistor superspace $\mathbf{MT}^{2|\mathcal{N}}$. We demonstrate that the semiclassical effective action of these $\sigma$-models reproduces the MHV gluonic and gravitational leaf amplitudes in $\mathcal{N}=4$ SYM theory and $\mathcal{N}=8$ Supergravity. This construction provides a concrete realisation of the supersymmetric celestial CFT framework recently introduced by Tropper (2024).