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Geometry-Kinematics Duality

Cheung, Clifford and Helset, Andreas and Parra-Martinez, Julio (2022) Geometry-Kinematics Duality. . (Unpublished)

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We propose a mapping between geometry and kinematics that implies the classical equivalence of any theory of massless bosons -- including spin and exhibiting arbitrary derivative or potential interactions -- to a nonlinear sigma model (NLSM) with a momentum-dependent metric in field space. From this kinematic metric we construct a corresponding kinematic connection, covariant derivative, and curvature, all of which transform appropriately under general field redefinitions, even including derivatives. We show explicitly how all tree-level on-shell scattering amplitudes of massless bosons are equal to those of the NLSM via the replacement of geometry with kinematics. Lastly, we describe how the recently introduced geometric soft theorem of the NLSM, which universally encodes all leading and subleading soft scalar theorems, also captures the soft photon theorems.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper ItemJournal Article
Cheung, Clifford0000-0002-9983-9425
Helset, Andreas0000-0002-5904-3748
Parra-Martinez, Julio0000-0003-0178-1569
Additional Information:C.C., A.H., and J.P.-M. are supported by the DOE under grant no. DE-SC0011632 and by the Walter Burke Institute for Theoretical Physics. We are grateful to Zvi Bern, Enrico Herrmann, James Mangan, Aneesh Manohar, and Ira Rothstein for comments on the draft.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
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Record Number:CaltechAUTHORS:20220707-170611265
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115377
Deposited By: George Porter
Deposited On:08 Jul 2022 23:02
Last Modified:20 Sep 2022 18:08

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