Twisted holography without conformal symmetry

We discuss the notion of translation-invariant vacua for 2d chiral algebras and relate it to the notion of the associated variety. The two-dimensional chiral algebra associated to four-dimensional ${\cal N}=4$ $U(N)$ SYM has a conjectural holographic dual involving the B-model topological string theory. We study the effect of non-zero vacuum expectation values on the chiral algebra correlation functions and derive a holographic dual Calabi-Yau geometry. We test our proposal by a large $N$ analysis of correlation functions of determinant operators, whose saddles can be matched with semi-classical configurations of "Giant Graviton" D-branes in the bulk