Gravitational boundary modes in AdS and flat space

To understand the structure of the Hilbert space of gravitational theories, an important and universal sector is given by the “large gauge” modes, which live on (asymptotic) boundaries. I will discuss two examples. The first are the so-called boundary gravitons in AdS3. Leveraging the duality to the T-Tbar deformation, we can extract the symmetries and (non)-locality properties of gravity beyond asymptotically AdS. As a second example, I will consider the IR sector of gauge theories in flat space, where one can construct a generating function for the S-matrix which is invariant under certain asymptotic symmetries. I will show that this invariance is nothing but the associated soft theorem.