Conference

I will describe shortly what the higher-spin charges are and why they are relevant from a holographic point of view. Besides, I will emphasize the recent result according to which they are realized as Noether charges in a non-linear regime.

Based on an idea of Kevin Costello, I will show how to construct a double cover of the twistor space of $\mathbb{R}^4$, $X = \pi^*(\mathcal{O}(1)\oplus\mathcal{O}(1))\to\Sigma$ where $\Sigma$ is an (hyper)elliptic curve. I then discuss how holomorphic theories such as BF and Chern-Simons theory on $X$ descend to theories on ordinary twistor space. Once on twistor space, compactifying along the $\mathbb{CP}^1$ direction of twistor space produces a corresponding 4d theory where we can study the algebra of collinear singularities. I will present my calculations which show that this algebra lives on the elliptic curve defining the double cover of twistor space.

We show that a 2D CFT consisting of a central charge c Liouville theory, a chiral level one, rank N Kac-Moody algebra and a weight −3/2 free fermion holographically generates 4D MHV leaf amplitudes associated to a single hyperbolic slice of flat space. Celestial amplitudes arise in a large-N and semiclassical large-c limit, according to the holographic dictionary, as a translationally-invariant combination of leaf amplitudes. A step in the demonstration is showing that the semiclassical limit of Liouville correlators are given by contact AdS3 Witten diagrams.

This talk is based on work in progress with Giuseppe Bogna. We consider the twistor description of classical self-dual Einstein gravity in the presence of a cosmological constant and a defect operator wrapping a certain $\mathbb{CP}^1$. The backreaction of this defect deforms the flat twistor space to that of quaternionic Taub-NUT space, a certain self-dual limit of a family of Kerr Taub-NUT AdS black holes. We discuss a 2-parameter family of Lie-algebras depending on the mass of the black hole and the cosmological constant. In various limits it reduces to algebras which were previously studied in the context of celestial holography and are closely related to $w_{1+\infty}$.