  In this note, we study a simplified variant of the familiar holographic
duality between supergravity on AdS$_3\times S^3\times T^4$ and the SCFT (on
the moduli space of) the symmetric orbifold theory $Sym^N(T^4)$ as $N
\rightarrow \infty$. This variant arises conjecturally from a twist proposed by
the first author and Si Li. We recover a number of results concerning protected
subsectors of the original duality working directly in the twisted bulk theory.
Moreover, we identify the symmetry algebra arising in the $N\rightarrow \infty$
limit of the twisted gravitational theory. We emphasize the role of
$\textit{Koszul duality}$---a ubiquitous mathematical notion to which we
provide a friendly introduction---in field theory and string theory. After
illustrating the appearance of Koszul duality in the "toy" example of
holomorphic Chern-Simons theory, we describe how (a deformation of) Koszul
duality relates bulk and boundary operators in our twisted setup, and explain
how one can compute algebra OPEs diagrammatically using this notion. Further
details, results, and computations will appear in a companion paper.
