The CEGM NLSM
Abstract Studying quantum field theories through geometric principles has revealed deep connections between physics and mathematics, including the discovery by Cachazo, Early, Guevara and Mizera (CEGM) of a generalization of biadjoint scalar amplitudes. However, extending this to generalizations of...
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SpringerOpen
2025-04-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP04(2025)030 |
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| author | Nick Early |
| author_facet | Nick Early |
| author_sort | Nick Early |
| collection | DOAJ |
| description | Abstract Studying quantum field theories through geometric principles has revealed deep connections between physics and mathematics, including the discovery by Cachazo, Early, Guevara and Mizera (CEGM) of a generalization of biadjoint scalar amplitudes. However, extending this to generalizations of other quantum field theories remains a central challenge. Recently it has been discovered that the nonlinear sigma model (NLSM) emerges after a certain zero-preserving deformation from tr(ϕ 3). In this work, we find a much richer story of zero-preserving deformations in the CEGM context, yielding generalized NLSM amplitudes. We prove an explicit formula for the residual embedding of an n-point NLSM amplitude in a mixed n + 2 point generalized NLSM amplitude, which provides a strong consistency check on our generalization. We show that the dimension of the space of pure kinematic deformations is gcd(k, n) − 1, we introduce a deformation-compatible modification of the Global Schwinger Parameterization, and we include a new proof, using methods from matroidal blade arrangements, of the linear independence for the set of planar kinematic invariants for CEGM amplitudes. Our framework is compatible with string theory through recent generalizations of the Koba-Nielsen string integral to any positive configuration space X +(k, n), where the usual Koba-Nielsen string integral corresponds to X(2, n) = M 0 , n $$ {\mathcal{M}}_{0,n} $$ . |
| format | Article |
| id | doaj-art-48642ac6aafa41098e4cbea45ffce5af |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-48642ac6aafa41098e4cbea45ffce5af2025-08-20T02:15:01ZengSpringerOpenJournal of High Energy Physics1029-84792025-04-012025412910.1007/JHEP04(2025)030The CEGM NLSMNick Early0Institute for Advanced StudyAbstract Studying quantum field theories through geometric principles has revealed deep connections between physics and mathematics, including the discovery by Cachazo, Early, Guevara and Mizera (CEGM) of a generalization of biadjoint scalar amplitudes. However, extending this to generalizations of other quantum field theories remains a central challenge. Recently it has been discovered that the nonlinear sigma model (NLSM) emerges after a certain zero-preserving deformation from tr(ϕ 3). In this work, we find a much richer story of zero-preserving deformations in the CEGM context, yielding generalized NLSM amplitudes. We prove an explicit formula for the residual embedding of an n-point NLSM amplitude in a mixed n + 2 point generalized NLSM amplitude, which provides a strong consistency check on our generalization. We show that the dimension of the space of pure kinematic deformations is gcd(k, n) − 1, we introduce a deformation-compatible modification of the Global Schwinger Parameterization, and we include a new proof, using methods from matroidal blade arrangements, of the linear independence for the set of planar kinematic invariants for CEGM amplitudes. Our framework is compatible with string theory through recent generalizations of the Koba-Nielsen string integral to any positive configuration space X +(k, n), where the usual Koba-Nielsen string integral corresponds to X(2, n) = M 0 , n $$ {\mathcal{M}}_{0,n} $$ .https://doi.org/10.1007/JHEP04(2025)030Differential and Algebraic GeometryScattering Amplitudes |
| spellingShingle | Nick Early The CEGM NLSM Journal of High Energy Physics Differential and Algebraic Geometry Scattering Amplitudes |
| title | The CEGM NLSM |
| title_full | The CEGM NLSM |
| title_fullStr | The CEGM NLSM |
| title_full_unstemmed | The CEGM NLSM |
| title_short | The CEGM NLSM |
| title_sort | cegm nlsm |
| topic | Differential and Algebraic Geometry Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP04(2025)030 |
| work_keys_str_mv | AT nickearly thecegmnlsm AT nickearly cegmnlsm |