Anomaly Cancellation and gauge group of the standard model in NCG

TL;DR

This paper explores how in noncommutative geometry, anomaly cancellation conditions precisely determine the gauge group of the standard model, linking unimodularity to anomaly cancellation and symmetry reduction.

Contribution

It establishes a strict equivalence between unimodularity and anomaly cancellation in Connes' NCG framework, clarifying the origin of the standard model gauge group.

Findings

Unimodularity condition is equivalent to anomaly cancellation.

Anomaly cancellation reduces the gauge symmetry to SU(3)×SU(2)×U(1).

Hypercharge assignments are almost determined by anomaly cancellation.

Abstract

It is well known that anomaly cancellation {\it almost} determines the hypercharges in the standard model. A related (and somewhat more stronger) phenomenon takes place in Connes' NCG framework: unimodularity (a technical condition on elements of the algebra) is {\it strictly} equivalent to anomaly cancellation (in the absence of right-handed neutrinos); and this in turn reduces the symmetry group of the theory to the standard $SU(3)\times SU(2) \times U(1)$.