Quantum Gravity Boundary Terms from Spectral Action of Noncommutative Space

TL;DR

This paper demonstrates that the spectral action of a noncommutative space, modeling the standard model, uniquely predicts the gravitational boundary term necessary for quantum gravity consistency, with correct sign and coefficient.

Contribution

It proves that the spectral action inherently determines the gravitational boundary term, reducing the need for arbitrary tuning in quantum gravity models.

Findings

Spectral action predicts the gravitational boundary term uniquely.

The boundary term has the correct sign and coefficient.

This result supports the consistency of quantum gravity within noncommutative geometry.

Abstract

We study the boundary terms of the spectral action of the noncommutative space, defined by the spectral triple dictated by the physical spectrum of the standard model, unifying gravity with all other fundamental interactions. We prove that the spectral action predicts uniquely the gravitational boundary term required for consistency of quantum gravity with the correct sign and coefficient. This is a remarkable result given the lack of freedom in the spectral action to tune this term.