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What is the Geometry of Effective Field Theories?
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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.
Forward citations
Cited by 3 Pith papers
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geoSCET: Soft Theorems from Power Counting
geoSCET derives geometric soft theorems for scalar field theories directly from effective-field-theory power counting and proves they are exact to all orders in perturbation theory when no potential is present.
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Geometry of soft scalars at one loop
The geometric soft theorem for scalar effective field theories is unchanged at one loop in derivative-coupled theories, and receives a universal leading correction when potential interactions are present.
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Renormalizing Two-Fermion Operators in the SMEFT via Supergeometry
A covariant one-loop divergence formula for mixed boson-fermion graphs is derived and applied to dimension-eight two-fermion RGEs in the SMEFT.
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