Asymptotic Symmetries, Black Holes, and Holography

Explore the deep connections between asymptotic symmetries, black holes, and holographic duality in this comprehensive lecture series that examines how gauge transformations at boundaries lead to infinite-dimensional symmetry groups with profound implications for quantum gravity. Learn how Emmy Noether's theorem extends to gauge theories with boundaries, where gauge parameters that don't vanish at infinity create non-trivial asymptotic symmetries acting on physical state spaces. Master the covariant phase space formalism for constructing conserved charges and discover how these symmetries naturally emerge in holographic correspondences as global symmetries of dual field theories. Investigate specific gravitational backgrounds including AdS_3 spacetime, near-horizon regions of extreme black holes, and flat spacetime, each exhibiting infinite-dimensional asymptotic symmetry groups. Understand the parallel development connecting asymptotic symmetries to soft behavior in scattering amplitudes, providing fresh perspectives on established results in quantum field theory. Examine the relationship between supertranslations, superrotations, and gravitational memory effects in flat space, while exploring how scattering symmetries relate to soft theorems. Gain insight into how asymptotic symmetry analysis may illuminate the nature of dual field theories in holographic scenarios beyond the well-established AdS/CFT correspondence, particularly for spacetimes where holographic duality remains poorly understood.