What is the geometry of effective field theories?

Cohen, Timothy; Lu, Xiaochuan; Zhang, Zhengkang

doi:10.1103/PhysRevD.111.085012

What is the geometry of effective field theories?

Journal Article · Mon Apr 07 00:00:00 EDT 2025 · Physical Review. D.

DOI:https://doi.org/10.1103/PhysRevD.111.085012· OSTI ID:2550672

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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 Society 2025

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0009919; SC0011640

OSTI ID:: 2550672

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 8 Vol. 111; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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