In this note, we study a simplified variant of the familiar holographic duality between supergravity on AdS$_3times S^3times T^4$ 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 $Nrightarrow infty$ 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.
تحميل البحث