Spectral action beyond the weak-field approximation

TL;DR

This paper computes the spectral action for non-compact spectral triples under gauge perturbations up to second order, revealing its decay behavior in the ultraviolet regime across even dimensions.

Contribution

It provides a covariant computation of the spectral action beyond the weak-field approximation for non-compact spectral triples.

Findings

Spectral action computed covariantly up to second order.

Action decays as 1/p^4 in the ultraviolet regime.

Results hold in any even dimension.

Abstract

The spectral action for a non-compact commutative spectral triple is computed covariantly in a gauge perturbation up to order 2 in full generality. In the ultraviolet regime, $p\to\infty$, the action decays as $1/p^4$ in any even dimension.