Abstract
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 that 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.
Highlights
Introduction.—Whenever a classical symmetry of a quantum field theory is broken by quantum corrections it is said to exhibit an anomaly
The amplitudes sourced by the anomaly, when inserted into unitarity cuts at higher loops, lead to potential ultraviolet divergent contributions [7], which cancel at three loops [12], but not at four loops [13]. Another connection is the recent observation that the anomalous amplitudes are intertwined with evanescent contributions [15], similar to those which played an important role in the interpretation of the two-loop ultraviolet divergence of pure Einstein gravity in dimensional regularization [16,17]
Evanescent operators—such as the Gauss-Bonnet R2 operator—are those whose tree-level matrix elements vanish identically in four but not general dimensions. They can contribute to divergences in dimensional regularization while otherwise having no physical consequences in the amplitudes, since their effects can be removed by the addition of local counterterms [18]
Summary
Introduction.—Whenever a classical symmetry of a quantum field theory is broken by quantum corrections it is said to exhibit an anomaly. They can contribute to divergences in dimensional regularization while otherwise having no physical consequences in the amplitudes, since their effects can be removed by the addition of local counterterms [18]. From the perspective of the double-copy construction of N 1⁄4 4 supergravity [19,20], in terms of N 1⁄4 4 super-Yang-Mills and pure Yang-Mills theory, both these and the anomalous contributions originate in the same rational pieces of the corresponding Yang-Mills amplitudes.
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