To renormalize QFT on curved spacetime with an external two-form background, one must add the scalar coupling ξ2 B^2 φ^2, as confirmed by a one-loop SU(2) calculation that generates this divergence; the coupling grows in the UV.
Local conformal symmetry and anomalies with antisymmetric tensor field
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We consider the trace anomaly, which results from the integration of the massless conformal fermion field with the background of metric and antisymmetric tensor fields. The non-local terms in the anomaly-induced effective action do not depend on the scheme of quantum calculations. On the other hand, total derivative terms in the anomaly and the corresponding local part of the induced action manifest scheme dependence and multiplicative anomaly.
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Renormalizable quantum field theory in curved spacetime with external two-form field
To renormalize QFT on curved spacetime with an external two-form background, one must add the scalar coupling ξ2 B^2 φ^2, as confirmed by a one-loop SU(2) calculation that generates this divergence; the coupling grows in the UV.