Abstract
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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Acknowledgments
We would like to thank John Celestial, Grant Remmen, and Chia-Hsien Shen for useful discussions, and Tim Cohen for collaboration at early stages of this work. The work of NC and YL was supported in part by the U.S. Department of Energy under the grant DE-SC0011702 and performed in part at the Kavli Institute for Theoretical Physics, supported by the National Science Foundation under Grant No. NSF PHY-1748958. The work of XL is supported by the U.S. Department of Energy under grant number DE-SC0009919.
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Craig, N., Lee, YT., Lu, X. et al. Effective field theories as Lagrange spaces. J. High Energ. Phys. 2023, 69 (2023). https://doi.org/10.1007/JHEP11(2023)069
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DOI: https://doi.org/10.1007/JHEP11(2023)069