TY - JOUR

T1 - On the U(1) duality anomaly and the S-matrix of ̄ 4 supergravity

AU - Carrasco, John Joseph

AU - Kallosh, R.

AU - Roiban, R.

AU - Tseytlin, A. A.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Anomalies in Field and String Theories

KW - Extended Supersymmetry

KW - Supersymmetry and Duality

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UR - http://www.scopus.com/inward/citedby.url?scp=84881318736&partnerID=8YFLogxK

U2 - 10.1007/JHEP07(2013)029

DO - 10.1007/JHEP07(2013)029

M3 - Article

AN - SCOPUS:84881318736

VL - 2013

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 7

M1 - 29

ER -