Inner fluctuations and the spectral Einstein functional

TL;DR

This paper extends spectral functionals related to Dirac operators by introducing new spectral functionals and computes the spectral Einstein functional for Dirac operators with inner fluctuations on even-dimensional spin manifolds.

Contribution

It introduces new spectral functionals extending existing ones and calculates the spectral Einstein functional in the context of inner fluctuations of Dirac operators.

Findings

Computed spectral Einstein functional for Dirac operators with inner fluctuations

Extended spectral functionals for Dirac operators

Provided explicit formulas on even-dimensional spin manifolds

Abstract

The spectral metric and Einstein functionals defined by two vector fields and Laplace-type operators over vector bundles, giving an interesting example of the spinor connection and square of the Dirac operator. Motivated by the spectral functionals and Dirac operators with inner fluctuations, we give some new spectral functionals which is the extension of spectral functionals for Dirac operators, and compute the spectral Einstein functional for the Dirac operator with inner fluctuations on even-dimensional spin manifolds without boundary.