The Kastler–Kalau–Walze-type theorems about J-Witten deformation

In this paper, we obtain a Lichnerowicz-type formula for [Formula: see text]-Witten deformation and give the proof of the Kastler–Kalau–Walze-type theorems associated with [Formula: see text]-Witten deformation on four-dimensional and six-dimensional almost product Riemannian manifold with (respectively, without) boundary. We give an explanation of the Einstein–Hilbert action for [Formula: see text]-Witten deformation on four-dimensional manifold with boundary.