Towards a Celestial Theory of Gravity, Gauge Theory, and Black Holes

Abstract

The search for a consistent theory of quantum gravity in four-dimensional (4D) asymptotically flat spacetimes has led to the development of celestial holography, a framework in which 4D scattering amplitudes are recast as correlation functions in a two-dimensional (2D) conformal field theory living on the celestial sphere. This dissertation contributes new entries to this 4D--2D holographic dictionary, with applications to scattering theory, black holes, and aspects of supersymmetric gauge theories. We begin by establishing a concrete correspondence between bulk scattering states and boundary CFT states. Boundary states can be constructed via the state-operator correspondence, where the celestial inner products are formulated from bulk inner products using a combination of shadow transforms and BPZ conjugation. This 2D reformulation organizes the scattering problem in a dramatically different way than in the 4D bulk, by mapping states between the hemispheres of the 2D boundary. Next, we develop a direct map between black hole geometries and scattering amplitudes in $(2,2)$ signature, showing how linearized black hole spacetimes such as Kerr-Taub-NUT can be obtained from three-point graviton emission amplitudes. We also study the global structure of $(2,2)$ black holes via toric Penrose diagrams and show that the Kerr rotation parameter, $a$, can be eliminated by a large diffeomorphism. Following from these black hole results, we derive the celestial CFT dual of 4D linearized rotating self-dual black holes. This is accomplished by identifying the corresponding 2D ``black hole'' states as global conformal primaries on the celestial torus. These can be realized as coherent states of Goldstone modes, carrying an infinite tower of soft hair. We also draw connections to Wilson lines and celestial scattering in curved backgrounds. Finally, we take steps towards the celestial dual for supersymmetric $\mathcal{N}=2$ gauge theories. We find that the soft sector of these theories is realized as a chiral algebra on the boundary, and that the bulk electric-magnetic duality is realized as SL$_2(\mathbb{Z})$ covariance of the celestial symmetry algebra. We also explore the boundary interpretation of the bulk moduli space singularities in terms of vertex operators constructed from soft and Goldstone modes.