Even-point multi-loop unitarity and its applications: exponentiation, anomalies and evanescence
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 prop...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-01-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP01(2024)019 |
| _version_ | 1797363740985786368 |
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| author | John Joseph M. Carrasco Nicolas H. Pavao |
| author_facet | John Joseph M. Carrasco Nicolas H. Pavao |
| author_sort | John Joseph M. Carrasco |
| collection | DOAJ |
| description | 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 CP $$ \mathbbm{CP} $$ 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 N $$ \mathcal{N} $$ = 4 DBIVA superfields. Finally we find that N $$ \mathcal{N} $$ = 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 N $$ \mathcal{N} $$ = 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. |
| first_indexed | 2024-03-08T16:24:59Z |
| format | Article |
| id | doaj.art-896e405d39a34876b5d01a8c560a26a8 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-08T16:24:59Z |
| publishDate | 2024-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-896e405d39a34876b5d01a8c560a26a82024-01-07T12:05:45ZengSpringerOpenJournal of High Energy Physics1029-84792024-01-012024116910.1007/JHEP01(2024)019Even-point multi-loop unitarity and its applications: exponentiation, anomalies and evanescenceJohn Joseph M. Carrasco0Nicolas H. Pavao1Department of Physics and Astronomy, Northwestern UniversityDepartment of Physics and Astronomy, Northwestern UniversityAbstract 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 CP $$ \mathbbm{CP} $$ 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 N $$ \mathcal{N} $$ = 4 DBIVA superfields. Finally we find that N $$ \mathcal{N} $$ = 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 N $$ \mathcal{N} $$ = 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.https://doi.org/10.1007/JHEP01(2024)019Scattering AmplitudesEffective Field TheoriesAnomalies in Field and String Theories |
| spellingShingle | John Joseph M. Carrasco Nicolas H. Pavao Even-point multi-loop unitarity and its applications: exponentiation, anomalies and evanescence Journal of High Energy Physics Scattering Amplitudes Effective Field Theories Anomalies in Field and String Theories |
| title | Even-point multi-loop unitarity and its applications: exponentiation, anomalies and evanescence |
| title_full | Even-point multi-loop unitarity and its applications: exponentiation, anomalies and evanescence |
| title_fullStr | Even-point multi-loop unitarity and its applications: exponentiation, anomalies and evanescence |
| title_full_unstemmed | Even-point multi-loop unitarity and its applications: exponentiation, anomalies and evanescence |
| title_short | Even-point multi-loop unitarity and its applications: exponentiation, anomalies and evanescence |
| title_sort | even point multi loop unitarity and its applications exponentiation anomalies and evanescence |
| topic | Scattering Amplitudes Effective Field Theories Anomalies in Field and String Theories |
| url | https://doi.org/10.1007/JHEP01(2024)019 |
| work_keys_str_mv | AT johnjosephmcarrasco evenpointmultiloopunitarityanditsapplicationsexponentiationanomaliesandevanescence AT nicolashpavao evenpointmultiloopunitarityanditsapplicationsexponentiationanomaliesandevanescence |