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On the U(1) duality anomaly and the S-matrix of \( \mathcal{N} \) = 4 supergravity

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Abstract

\( \mathcal{N} \) = 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 \( \mathcal{N} \) = 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 \( \mathcal{N} \) = 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 \( \mathcal{N} \) = 4 supergravity amplitudes that have non-vanishing soft-scalar limits (these amplitudes are absent in \( \mathcal{N} \) > 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.

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Authors and Affiliations

  1. Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, 382 Via Pueblo Mall, Stanford, CA, 94305-4060, U.S.A

    J. J. M. Carrasco & R. Kallosh

  2. Department of Physics, The Pennsylvania State University, University Park, PA, 16802, U.S.A

    R. Roiban

  3. Blackett Laboratory, Imperial College, Prince Consort Road, London, SW7 2AZ, U.K

    A. A. Tseytlin

  4. Lebedev Institute, Moscow, Russia

    A. A. Tseytlin

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  1. J. J. M. Carrasco
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  2. R. Kallosh
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  3. R. Roiban
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  4. A. A. Tseytlin
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Correspondence to R. Roiban.

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ArXiv ePrint: 1303.6219

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Carrasco, J.J.M., Kallosh, R., Roiban, R. et al. On the U(1) duality anomaly and the S-matrix of \( \mathcal{N} \) = 4 supergravity. J. High Energ. Phys. 2013, 29 (2013). https://doi.org/10.1007/JHEP07(2013)029

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