On the map induced on Hochschild homology of matrix factorization categories by the inclusion of a divisor

Abstract: Given a smooth variety $X$ over $\mathbb{C}$, a smooth divisor $i:Y\hookrightarrow X$ and a global function $f$ on $X$ which vanishes on $Y$ and on its critical locus we compute the map induced on Hochschild homology by the pushforward functor $i_*:D^b(Y)\to D^{abs}(MF(X,f))$ in terms of the Hochschild-Kostant-Rosenberg isomorphisms.