Categorical 't Hooft expansion and chiral algebras

Twisted holography captures protected aspects of well-known holographic dualities. We show how the holographic dual B-model background can be systematically derived from the 't Hooft expansion of the chiral algebras associated to four-dimensional ${\cal N}=2$ superconformal quiver gauge theories. A crucial tool is the match of planar BRST anomalies in the field theory and on the worldsheet, especially in the presence of probe D-branes. Our construction is very general and can be applied to chiral algebras which do not have a four-dimensional origin. The resulting holographic dual backgrounds are typically non-geometric and appear to be novel. We expect our strategy to have a wide range of applications to other examples of twisted holography and, potentially, weak coupling holography.