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We elaborate on a recently proposed geometric framework for scalar effective field theories. Starting from the action, a metric can be identified that enables the construction of geometric quantities on the associated functional manifold. These objects transform covariantly under general field redefinitions that relate different operator bases, including those involving derivatives. We present a novel geometric formula for the amplitudes of the theory, where the vertices in Feynman diagrams are replaced by their geometrized counterparts. This makes the on-shell covariance of amplitudes manifest, providing the link between functional geometry and effective field theories. Published by the American Physical Society2025
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This content will become publicly available on February 1, 2027
Geometric building blocks of effective field theory amplitudes
A<sc>bstract</sc> On-shell amplitudes are invariant under field redefinitions. Nonderivative field redefinitions have a natural interpretation as coordinate transformations on the target manifold. General field redefinitions, which may involve derivatives, can be viewed as coordinate transformations on the field configuration manifold. We present a unified perspective for the geometry of both the target manifold and the field configuration manifold for scalar effective field theories. In both cases, we identify vertices that can be used to build the tree-level amplitudes, with the property that they transform covariantly in the vacuum and on-shell limits. We identify a choice of metric on the field configuration manifold, for which amplitude expressions on the target manifold can be easily reproduced from their counterparts on the field configuration manifold. This clarifies the relation between the well-established framework of field space geometry and recent proposals for functional geometry.
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- Award ID(s):
- 2412880
- PAR ID:
- 10697866
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2026
- Issue:
- 2
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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