### Abstract

4 Poincaré supergravity has a global SU(1, 1) duality symmetry that acts manifestly only on shell as it involves duality rotations of vector fields. A U(1) subgroup of this symmetry is known to be anomalous at the quantum level in the presence of a non-trivial gravitational background. We first derive this anomaly from a novel perspective, by relating it to a similar anomaly in conformal supergravity where SU(1, 1) acts off shell, using the fact that 4 Poincaré supergravity has a superconformal formulation. We explicitly construct the corresponding local and nonlocal anomalous terms in the one-loop effective action. We then study how this anomaly is reflected in the supergravity S-matrix. Calculating one-loop 4 supergravity scattering amplitudes (with and without additional matter multiplets) using color/kinematics duality and the double-copy construction we find that a particular U(1) symmetry which was present in the tree-level amplitudes is broken at the quantum level. This breaking manifests itself in the appearance of new one-loop 4 supergravity amplitudes that have non-vanishing soft-scalar limits (these amplitudes are absent in > 4 supergravities). We discuss the relation between these symmetry-violating amplitudes and the corresponding U(1) anomalous term in the one-loop supergravity effective action.

Original language | English (US) |
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Article number | 29 |

Journal | Journal of High Energy Physics |

Volume | 2013 |

Issue number | 7 |

DOIs | |

State | Published - Jan 1 2013 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

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## Cite this

*Journal of High Energy Physics*,

*2013*(7), [29]. https://doi.org/10.1007/JHEP07(2013)029