Bottom-up and top-down aspects of celestial CFT

The holographic principle suggests that quantum gravity on a manifold M can be described by degrees of freedom living on its boundary ∂M. While the AdS/CFT correspondence provides a concrete realization of this idea, extending holography to asymptotically flat spacetime remains an open problem. The celestial holography program proposes that gravity in four-dimensional flat space is dual to a two-dimensional conformal field theory, known as celestial CFT (CCFT). This thesis provides valuable insights to two key questions in this framework: the structure of the CCFT spectrum and the possibility to build a top-down construction of the dual model. We show that the observed vanishing central charge in CCFT points beyond unitary CFTs, toward logarithmic CFTs (LCFTs). Through a bottom-up analysis of tree-level amplitudes, we demonstrate that logarithmic operators naturally arise from infrared regularization, explaining the logarithmic nature of CCFT and constraining its primary spectrum. We also develop a top-down approach by constructing the celestial dual for MHV leaf amplitudes, extending recent proposals. This provides new insights into the role of asymptotic symmetries, stress tensor structure, and celestial OPEs, bringing us closer to a concrete flat space holographic duality. Our results support the idea that celestial CFT is realized through a non-standard two- dimensional theory, linking asymptotic symmetries, infrared dynamics, and logarithmic structures in quantum gravity.