Equivariant Matrix Factorizations and Hamiltonian reduction

Let $X$ be a smooth scheme with an action of an algebraic group $G$. We establish an equivalence of two categories related to the corresponding moment map $μ: T^*X \to Lie(G)^*$ - the derived category of G-equivariant coherent sheaves on the derived fiber $μ^{-1}(0)$ and the derived category of $G$-equivariant matrix factorizations on $T^*X \times Lie(G)$ with potential given by $μ$.

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