Anomaly Cancellation and Conformality in Quiver Gauge Theories

Abstract

Abelian quiver gauge theories provide nonsupersymmetric candidates for the conformality approach to physics beyond the standard model. Written as $\mathcal{N}=0$, $U(N{)}^n$ 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 $\Delta {\mathcal{L}}_{comp}$ which restores gauge invariance of ${\mathcal{L}}_{eff}=\mathcal{L}+\Delta {\mathcal{L}}_{comp}$ 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.

15 pages. minor clarifications

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