Non-Abelian Anomalies and Effective Actions for a Homogeneous Space $G/H$

Details Non-Abelian Anomalies and Effective Actions for a Homogeneous Space $G/H$ Non-Abelian Anomalies and Effective Actions for a Homogeneous Space $G/H$

1996-02-16

arxiv.org/abs/hep-th/9602093v2

Nucl.Phys. B475 (1996) 484-504

Physics

High Energy Physics

High Energy Physics - Theory

revised

Scientific paper

10.1016/0550-3213(96)00322-7

We consider the problem of constructing the fully gauged effective action in $2n$-dimensional space-time for Nambu-Goldstone bosons valued in a homogeneous space $G/H$, with the requirement that the action be a solution of the anomalous Ward identity and be invariant under the gauge transformations of $H$. We show that this can be done whenever the homotopy group $\pi_{2n}(G/H)$ is trivial, $G/H$ is reductive and $H$ is embedded in $G$ so as to be anomaly free, in particular if $H$ is an anomaly safe group. We construct the necessary generalization of the Bardeen counterterm and give explicit forms for the anomaly and the effective action. When $G/H$ is a symmetric space the counterterm and the anomaly decompose into a parity even and a parity odd part. In this case, for the parity even part of the action, one does not need the anomaly free embedding of $H$.

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