Cancelling the U(1) Anomaly in the S-matrix of N=4 Supergravity

Abstract

$\mathcal{N}=4$ supergravity is understood to contain a $U(1)$ anomaly which manifests itself via the nonvanishing of loop-level scattering amplitudes that violate a tree-level charge conservation rule. In this letter we provide detailed evidence that at one loop such anomalous amplitudes can be set to zero by the addition of a finite local counterterm. We show that the same counterterm also cancels evanescent contributions which play an important role in the analysis of ultraviolet divergences in dimensionally regularized gravity. These cancellations call for a reanalysis of the four-loop ultraviolet divergences previously found in this theory without the addition of such counterterms.

6 pages, journal version

References in corpus (14)

• New Relations for Gauge-Theory Amplitudes
• E7(7) constraints on counterterms in N=8 supergravity
• Gravity and Yang-Mills Amplitude Relations
• Stringy KLT relations, global symmetries, and E_7(7) violation
• On duality symmetries of supergravity invariants
• New Identities among Gauge Theory Amplitudes
• Two-Loop Renormalization of Quantum Gravity Simplified
• Construction of all N=4 conformal supergravities
• New Formulas for Amplitudes from Higher-Dimensional Operators
• Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
• Anomaly Cancellation in Supergravity with Fayet-Iliopoulos Couplings
• Absence of U(1) Anomalous Superamplitudes in $\mathcal{N}\ge 5$ Supergravities
• Cancellation of Conformal and Chiral Anomalies in $N\ge 5$ supergravities
• Anomaly Structure of Supergravity and Anomaly Cancellation

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• N=4 conformal supergravity: the complete actions
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• The Color-Dual Fates of $F^3$, $R^3$, and $\mathcal{N}=4$ Supergravity
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• Effective observables for electromagnetic duality from novel amplitude decomposition
• Gravity loop integrands from the ultraviolet
• Supersymmetry constraints on U-duality invariant deformations of $N\ge 5$ Supergravity
• The Action with Manifest E7 Type Symmetry
• Two-loop n-point anomalous amplitudes in N=4 supergravity
• $D$-Dimensional Modular Assembly of Higher-Derivative Four-Point Contact Amplitudes Involving Fermions