Abstract
In CP-violating conformal field theories in four dimensions, the Pontryagin density can appear in the Weyl anomaly. The Pontryagin density in the Weyl anomaly is consistent, but it has a peculiar feature that the parent three-point function of the energy-momentum tensor can violate CP only (semi-)locally. In this paper, we study the supersymmetric completion of the Pontryagin density in the Weyl anomaly, where the central charge $c$ effectively becomes a complex number. The supersymmetry suggests that it accompanies the graviphoton $\theta$ term associated with the R-symmetry gauging in the Weyl anomaly. It also accompanies new CP-violating terms in the R-current anomaly. While there are no conclusive perturbative examples of CP-violating super Weyl anomaly, we construct explicit supersymmetric dilaton effective action which generates these anomalies.
Highlights
Charge-parity (CP) symmetry and its breaking play fundamental roles in our understanding of our existence. It is the violation of the CP symmetry in the electroweak sector that enables us to generate nonzero baryon numbers, while we mysteriously observe the highly suppressed CP violation in the strong interaction sector of the standard model of particle physics
Within the Lagrangian description of quantum field theories, one can quantify the violation of the CP symmetry by examining the detailed structure of coupling constants: The Kobayashi-Maskawa matrix and θ term are such quantities in the electroweak and strong interaction sectors in the standard model
With the CP-violating Weyl anomaly, the central charge c, together with the Pontryagin density in the Weyl anomaly, is effectively complexified as the gauge coupling constant is complexified with the θ term in supersymmetric gauge theories
Summary
Charge-parity (CP) symmetry and its breaking play fundamental roles in our understanding of our existence. [1], it was pointed out that the Weyl anomaly in four-dimensional conformal field theories may include a term that is present only in CP-violating theories The Pontryagin density in the Weyl anomaly, has a peculiar feature that the parent three-point function of the energy-momentum tensor can violate CP only (semi)locally Such anomalies are called “impossible anomalies” in Ref. There have been active discussions if we may realize the Pontryagin density in the Weyl anomaly in concrete field theory examples With the CP-violating Weyl anomaly, the central charge c, together with the Pontryagin density in the Weyl anomaly, is effectively complexified as the gauge coupling constant is complexified with the θ term in supersymmetric gauge theories.
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