Conformal Perturbations of Twisted Dirac Operators and Noncommutative residue

TL;DR

This paper establishes new Kastler-Kalau-Walze type theorems for conformally perturbed twisted Dirac and signature operators on six-dimensional manifolds, including boundary cases, using non-unitary connections.

Contribution

It introduces novel theorems for conformal perturbations of twisted Dirac and signature operators with non-unitary connections on six-dimensional manifolds.

Findings

Derived Kastler-Kalau-Walze type theorems for boundary and non-boundary cases

Extended theorems to conformal perturbations with non-unitary connections

Applied results to six-dimensional manifolds

Abstract

In this paper, we obtain two kinds of Kastler-Kalau-Walze type theorems for conformal perturbations of twisted Dirac operators and conformal perturbations of signature operators by a vector bundle with a non-unitary connection on six-dimensional manifolds with (respectively without)boundary.