A Kastler-Kalau-Walze Type Theorem for 5-dimensional Manifolds with Boundary

TL;DR

This paper extends the Kastler-Kalau-Walze theorem to 5-dimensional manifolds with boundary, linking the Wodzicki residue of the Dirac operator to geometric invariants in higher dimensions.

Contribution

It proves a new Kastler-Kalau-Walze type theorem specifically for 5-dimensional manifolds with boundary, expanding the theorem's applicability.

Findings

Established the proportionality between Wodzicki residue and geometric invariants in 5D

Extended the theorem to manifolds with boundary

Provided mathematical framework for higher-dimensional generalizations

Abstract

The Kastler-Kalau-Walze theorem, announced by Alain Connes, shows that the Wodzicki residue of the inverse square of the Dirac operator is proportional to the Einstein-Hilbert action of general relativity. In this paper, we prove a Kastler-Kalau-Walze type theorem for 5-dimensional manifolds with boundary.