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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
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