Aspects of Symmetry for Flat Space Holography

Abstract

A central goal of modern high energy theory is to understand the structure of holographic dualities beyond asymptotically anti-de Sitter spacetimes. In asymptotically flat spacetimes, holographic dualities are expected to relate scattering amplitudes to correlation functions in a lower-dimensional theory living on the celestial sphere. However, it has proven challenging to construct examples of boundary theories with the full symmetry group of quantum gravity in flat spacetimes. In this thesis, we study how these bulk symmetries can emerge from lower-dimensional conformal field theories. After extending the celestial dictionary to (2,2)-signature Klein space, we show that fully Poincaré-invariant scattering amplitudes can emerge from building blocks of 2D CFTs. Next, we study how breaking translation invariance modifies the dual theory. We relate gluon scattering amplitudes in the presence of a translation-invariance breaking source to fundamental building blocks of the AdS/CFT correspondence. We then show that these translation- breaking backgrounds centrally extend the soft algebra of the dual theory, and use this to generate toy examples of celestial dualities for self-dual Yang-Mills with broken translation invariance. Finally, we study novel ways for Poincaré invariance to emerge from a lower-dimensional CFT. After showing that translation-invariant theories can emerge from entangled states in theories without translation invariance, we demonstrate that translation-invariant scattering amplitudes can be extracted from linear combinations of smooth CFT correlation functions. Ultimately, we construct an example where gluon scattering amplitudes can be extracted from a simple lower-dimensional theory