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Effective Field Theories as Lagrange Spaces
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We present a formulation of scalar effective field theories in terms of the geometry of Lagrange spaces. The horizontal geometry of the Lagrange space generalizes the Riemannian geometry on the scalar field manifold, inducing a broad class of affine connections that can be used to covariantly express and simplify tree-level scattering amplitudes. Meanwhile, the vertical geometry of the Lagrange space characterizes the physical validity of the effective field theory, as a torsion component comprises strictly higher-point Wilson coefficients. Imposing analyticity, unitarity, and symmetry on the theory then constrains the signs and sizes of derivatives of the torsion component, implying that physical theories correspond to a special class of vertical geometry.
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Cited by 3 Pith papers
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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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Tame Complexity of Effective Field Theories in the Quantum Gravity Landscape
Effective field theories consistent with quantum gravity are conjectured to have uniformly bounded 'tame complexity', a quantitative measure of the information needed to specify them.
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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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