A Kastler-Kalau-Walze Type Theorem for 7-dimensional Manifolds with Boundary about Witten deformation

In this paper, we give a brute-force proof of the Kastler-Kalau-Walze type theorem for $7$-dimensional manifolds with boundary about Witten deformation, and give a theoritic explaination of the gravitational action for $7$ dimensional manifolds with boundary.