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Anomaly cancellation and conformality in quiver gauge theories. (English) Zbl 1248.81210
Summary: Abelian quiver gauge theories provide non-supersymmetric candidates for the conformality approach to physics beyond the standard model. Written as $${\mathcal N}=0$$, $$\mathrm{U}(N)^n$$ gauge theories, however, they have mixed $$\mathrm{U}(1)_p\mathrm{U}(1)^2_q$$ and $$\mathrm{U}(1)_p\mathrm{SU}(N)^2_q$$ triangle anomalies. It is shown how to construct explicitly a compensatory term $$\Delta{\mathcal L}_{\mathrm{comp}}$$ which restores gauge invariance of $${\mathcal L}_{\mathrm{eff}}={\mathcal L}+\Delta{\mathcal L}_{\mathrm{comp}}$$ under $$\mathrm{U}(N)^n$$. It can lead to a negative contribution to the $$\mathrm{U}(1)$$ $$\beta$$-function and hence to one-loop conformality at high energy for all dimensionless couplings.

##### MSC:
 81T50 Anomalies in quantum field theory 81T13 Yang-Mills and other gauge theories in quantum field theory 81T17 Renormalization group methods applied to problems in quantum field theory
##### Keywords:
quiver gauge theories
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##### References:
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