Anomalous Current Due to Weyl Anomaly for Conformal Field Theory

Abstract

Recently it is found that Weyl anomaly leads to new anomalous currents in an external electromagnetic field in the curved spacetime. For simplicity, the initial works mainly focus on weak gravitational fields and the anomalous current is obtained for conformally flat spaces with small scale factors. In this paper, we generalize the results to the case with arbitrary scale factors. Firstly, we derive the transformation law of current under Weyl transformation, from which one can read off the anomalous current in general conformally flat spaces. Secondly, by using the Weyl transformation of currents we provide a new derivation of the Weyl-anomaly-induced current near the boundary. Thus we have obtained the two kinds of anomalous currents in the literature from a unified formula. Finally, we extend the discussions to n-form fields and find similar anomalous currents.

arXiv comment18 pages, 0 figure, match the published version in PLB

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• Dynamic scale anomalous transport in QCD with electromagnetic background
• Holographic Anomalous Chiral Current Near a Boundary
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• Chiral current induced by torsional Weyl anomaly
• Holographic Anomalous Current at a Finite Temperature
• Enhancement of Anomalous Boundary Current by High Temperature
• Remark on the synergy between the heat kernel techniques and the parity anomaly