Toward Supergravity Spectral Action

TL;DR

This paper introduces a spectral action framework for Euclidean supergravity, calculating key coefficients to advance the mathematical understanding of supergravity's spectral properties.

Contribution

It constructs a well-defined Dirac operator for supergravity and computes the Seeley-Dewitt coefficients up to a4, extending spectral action methods to supergravity.

Findings

Calculated Seeley-Dewitt coefficients up to a4 for supergravity

Established a consistent Dirac operator in supergravity

Extended spectral action techniques to supergravity context

Abstract

A spectral action of Euclidean supergravity is proposed. We calculate up to $a_4$, the Seeley-Dewitt coefficients in the expansion of the spectral action associated to the supergravity Dirac operator. This is possible because in simple supergravity, as in pure gravity, a well defined and mathematically consistent Dirac operator can be constructed.