Anomaly cancellation for anisotropic lattice fields with extra dimensions

TL;DR

This paper investigates how anomaly cancellation in anisotropic lattice gauge theories with extra dimensions depends on phase transitions and the presence of chiral zero modes, highlighting the role of the layered phase and gauge group structure.

Contribution

It clarifies the conditions under which anomaly cancellation occurs in lattice models with extra dimensions, emphasizing the importance of phase transitions and gauge group factors.

Findings

Anomaly cancellation is linked to the transition between layered and Coulomb phases.

The absence of current flow is due to the lack of chiral zero modes, not anomaly cancellation.

A compact U(1) gauge factor is necessary for anomaly cancellation along the transition line.

Abstract

The current flow from the bulk is due to the anomaly on the brane-but the absence of current flow is not, necessarily, due to anomaly cancellation, but to the absence of the chiral zero modes themselves, due to the existence of the layered phase. This can be understood in terms of the difference between the Chern-Simons terms in three and five dimensions. Thus the anomaly cancellation in four dimensions, which is essential for shielding the boundary from quantum effects within the bulk, makes sense only along the transition line between the layered and the Coulomb phase, which, in turn, requires the presence of a compact U(1) factor for the gauge group.