Spectral action, Weyl anomaly and the Higgs-Dilaton potential

TL;DR

This paper demonstrates how the bosonic spectral action arises from fermionic actions via renormalization group flow, incorporating a dilaton and Weyl anomaly, resulting in a gauge, Higgs, and gravity coupled spectral action with a viable effective potential.

Contribution

It shows the emergence of the spectral action from fermionic actions considering Weyl anomaly and dilaton, linking noncommutative geometry with physical gauge and Higgs fields.

Findings

Spectral action derived from fermionic action through RG flow.

Effective potential exhibits broken and unbroken phases.

Spectral action includes gauge, Higgs, and gravitational fields.

Abstract

We show how the bosonic spectral action emerges from the fermionic action by the renormalization group flow in the presence of a dilaton and the Weyl anomaly. The induced action comes out to be basically the Chamseddine-Connes spectral action introduced in the context of noncommutative geometry. The entire spectral action describes gauge and Higgs fields coupled with gravity. We then consider the effective potential and show, that it has the desired features of a broken and an unbroken phase, with the roll down.