Celestial and Matrix Holography for Flat-Space Quantum Gravity

Abstract

This thesis studies holography in asymptotically flat spacetimes through two complementary routes: a bottom-up approach based on celestial holography, and a top-down approach based on the BFSS matrix model. A central theme in both settings is how the full Poincar'e group and its extensions are encoded in dual variables. In the celestial direction, I construct an explicit bottom-up CFT dual for Yang-Mills amplitudes using leaf amplitudes associated with hyperbolic slices of flat space. These objects preserve Lorentz, or equivalently two-dimensional conformal, symmetry while temporarily relaxing translation invariance, allowing a concrete CFT description. The leaf amplitudes are then assembled to restore the full Poincar'e symmetry. I also develop complementary approaches to the problem of translations by constructing hyperbolic vacua in Minkowski space, the Poincar'e-invariant no-boundary state in Klein space, and a version of AdS/CFT adapted to time-periodic AdS$_3/\mathbb{Z}$ slices. Together, these results bridge key conceptual and technical gaps between flat and (A)dS holography, and represent a step toward quantum gravity in realistic spacetimes. In the BFSS matrix model, I uncover a rich, previously unknown infrared structure by translating soft graviton theorems from M-theory to the matrix model, matching scattering data on the two sides. In particular, I derive the complete set of Poincar'e charges in matrix degrees of freedom, and reveal an enhanced infinite-dimensional symmetry dual to the extended BMS group of supertranslations and superrotations. These symmetries manifest in the matrix model as large diffeomorphisms of the IIA metric and large gauge symmetries of the RR 1-form. This work resolves a major open problem in matrix-model kinematics, expands the holographic dictionary, and provides new nonperturbative evidence for the BFSS duality. More broadly, it demonstrates that symmetry-based approaches can extract exact results from microscopic theories that are otherwise computationally intractable.