Journal of Mathematical Physics, Analysis, Geometry
2021, vol. 17, No 2, pp. 119-145   https://doi.org/10.15407/mag17.02.119     ( to contents , go back )
https://doi.org/10.15407/mag17.02.119

A Kastler-Kalau-Walze Type Theorem for 7-Dimensional Manifolds with Boundary about Witten Deformation

Kai Hua Bao

School of Mathematics and Physics, Inner Mongolia University for the Nationalities, TongLiao, 028005, P. R. China
E-mail: baokh505@nenu.edu.cn

Ai Hui Sun

College of Mathematics, Jilin Normal University, Siping, 136000, P. R. China
E-mail: sunaihui2002@126.com

Kun Ming Hu

School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P. R. China
E-mail: 2943220150@qq.com

Received February 3, 2020, revised March 13, 2020.

Abstract

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

Mathematics Subject Classification 2010: 58G20, 53A30, 46L87
Key words: Witten deformation, noncommutative residue for manifolds with boundary, lower dimensional volumes

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