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

TL;DR

This paper provides a detailed proof of a Kastler-Kalau-Walze type theorem for 7-dimensional manifolds with boundary, incorporating Witten deformation, and offers a theoretical explanation of gravitational action in this context.

Contribution

It presents a brute-force proof of the theorem for 7D manifolds with boundary involving Witten deformation and explains the gravitational action theoretically.

Findings

Proof of Kastler-Kalau-Walze type theorem for 7D manifolds with boundary

Theoretical explanation of gravitational action in 7D boundary manifolds

Application of Witten deformation in the theorem

Abstract

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.