The Kastler-Kalau-Walze type theorem for 6-dimensional manifolds with boundary

TL;DR

This paper extends the Kastler-Kalau-Walze theorem to 6-dimensional spin manifolds with boundary, defining lower dimensional volumes and deriving boundary gravity via noncommutative residues of Dirac operators.

Contribution

It introduces a new Kastler-Kalau-Walze type theorem for 6D manifolds with boundary and computes associated lower dimensional volumes.

Findings

Computed the volume ${ m Vol}_{6}^{(1,3)}$ for 6D spin manifolds with boundary.

Derived boundary gravity from noncommutative residues.

Established a Kastler-Kalau-Walze type theorem for a general fourth order operator.

Abstract

In this paper, we define lower dimensional volumes of spin manifolds with boundary. We compute the lower dimensional volume ${\rm Vol}_{6}^{(1,3)}$ for 6-dimensional spin manifolds with boundary and the gravity on boundary is derived by the noncommutative residue associated with Dirac operators.For 6-dimensional manifolds with boundary, we also get a Kastler-Kalau-Walze type theorem for a general fourth order operator.