Spectral action with zeta function regularization

TL;DR

This paper introduces a new bosonic spectral action based on zeta function regularization, aiming to improve renormalizability and address spectral dimensions, while analyzing its physical implications and differences from traditional cutoff-based approaches.

Contribution

It proposes a novel zeta function regularized spectral action and explores its theoretical advantages and physical implications compared to the standard cutoff-based spectral action.

Findings

Zeta spectral action offers improved renormalizability.

Comparison shows differences with cutoff spectral action.

Neutrino Majorana mass is crucial for bosonic action structure.

Abstract

In this paper we propose a novel definition of the bosonic spectral action using zeta function regularization, in order to address the issues of renormalizability and spectral dimensions. We compare the zeta spectral action with the usual (cutoff based) spectral action and discuss its origin, predictive power, stressing the importance of the issue of the three dimensionful fundamental constants, namely the cosmological constant, the Higgs vacuum expectation value, and the gravitational constant. We emphasize the fundamental role of the neutrino Majorana mass term for the structure of the bosonic action.