Abstract
We identify novel structure in newly computed multi-loop amplitudes and quantum actions for even-point effective field theories, including both the nonlinear sigma model (NLSM) and double-copy gauge theories such as Born-Infeld and its supersymmetric generalizations. We exploit special properties of all even-point theories towards establishing an efficient unitarity based amplitude construction. In doing so, we find evidence that the leading IR divergence of NLSM amplitudes exponentiates when the target space is \( \mathbbm{CP} \)1 ≅ SU(2)/U(1). We then systematically compute the two-loop anomalous behavior of Born-Infeld, and find that the counterterms needed to restore U(1) invariant behavior at loop-level can be constructed via a symmetric-structure double-copy. We also demonstrate that the divergent part of the one-minus (−+++) two-loop anomaly vanishes upon introducing an evanescent operator. In addition to these purely photonic counterterms, we verify through explicit calculation that the anomalous matrix elements that violate U(1) duality invariance can be alternatively cancelled by summing over internal \( \mathcal{N} \) = 4 DBIVA superfields. Finally we find that \( \mathcal{N} \) = 4 Dirac-Born-Infeld-Volkov-Akulov (DBIVA) amplitudes admit double-copy construction through two-loop order by reproducing our unitarity based result with a double copy between color-dual \( \mathcal{N} \) = 4 super-Yang-Mills and our two-loop NLSM amplitudes. This result supports the possibility of color-dual representations for NLSM beyond one-loop. We conclude with an overview of how D-dimensional four-photon counterterms can be constructed in generality with the symmetric-structure double-copy, and outline a convenient way of counting evanescent operators using Hilbert series as generating functions.
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Acknowledgments
The authors would like to thank Rafael Aoude, Alex Edison, Kezhu Guo, Kays Haddad, Ian Low, James Mangan, Frank Petriello, Paolo Pichini, Nia Robles, Radu Roiban, Aslan Seifi, and Suna Zekioğlu for insightful conversations, related collaboration, and encouragement throughout the completion of this work. That authors additionally would like to thank James Mangan for incredibly thoughtful comments on earlier versions of the draft. The completion of this manuscript benefited from the hospitality of NORDITA during the workshop “Amplifying Gravity at All Scales”. This work was supported by the DOE under contract DE-SC0015910 and by the Alfred P. Sloan Foundation. N.H.P. acknowledges the Northwestern University Amplitudes and Insight group, the Department of Physics and Astronomy, and Weinberg College for their generous support.
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Carrasco, J.J.M., Pavao, N.H. Even-point multi-loop unitarity and its applications: exponentiation, anomalies and evanescence. J. High Energ. Phys. 2024, 19 (2024). https://doi.org/10.1007/JHEP01(2024)019
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DOI: https://doi.org/10.1007/JHEP01(2024)019