On Non-Local CFTs and Holography

t\bar T$ and $ J\bar T$ - deformed CFTs provide an interesting example of non-local, yet UV-complete two-dimensional QFTs that are entirely solvable. They are holographically dual to AdS$_3$ gravity with mixed boundary conditions for the non-dynamical metric, thus furnishing a fully controllable setup for checking the implications of asymptotic symmetry group analyses for such boundary conditions. In this talk, I will show that both $ T \bar T$ and $ J \bar T$ - deformed CFTs possess Virasoro x Virasoro or Virasoro- Kac- Moody x Virasoro - Kac- Moody symmetry, discuss the classical realization of these symmetries in terms of field-dependent coordinate transformations, and finally comment on their possibly non-standard holographic realization. Time permitting, I will discuss the analogous symmetries for symmetric product orbifolds of $ T \bar T$ and $ J \bar T$ - deformed CFTs, which are conjectured to capture holographic aspects of certain non-asymptotically AdS spacetimes.