Anomaly Cancellation and Conformality in Quiver Gauge Theories

TL;DR

This paper explores anomaly cancellation in non-supersymmetric quiver gauge theories, proposing a method to restore gauge invariance and achieve conformality at high energies through a compensatory term.

Contribution

It explicitly constructs a compensatory term to cancel anomalies in Abelian quiver gauge theories, enabling potential one-loop conformality.

Findings

Constructed a compensatory term for anomaly cancellation.

Restored gauge invariance of the effective Lagrangian.

Achieved negative contribution to the U(1) beta-function, supporting conformality.

Abstract

Abelian quiver gauge theories provide nonsupersymmetric candidates for the conformality approach to physics beyond the standard model. Written as ${\cal N}=0$, $U(N)^n$ gauge theories, however, they have mixed $U(1)_p U(1)_q^2$ and $U(1)_p SU(N)_q^2$ triangle anomalies. It is shown how to construct explicitly a compensatory term $\Delta{\cal L}_{comp}$ which restores gauge invariance of ${\cal L}_{eff} = {\cal L} + \Delta {\cal L}_{comp}$ under $U(N)^n$. It can lead to a negative contribution to the U(1) $\beta$-function and hence to one-loop conformality at high energy for all dimensionless couplings.