Infinite conformal symmetry and emergent chiral fields of topologically nontrivial configurations: From Yang-Mills-Higgs theory to the Skyrme model

Fabrizio Canfora, Diego Hidalgo, Marcela Lagos, Enzo Meneses, Aldo Vera

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9 Scopus citations

Abstract

In this manuscript, we discuss a remarkable phenomenon concerning nonlinear and nonintegrable field theories in (3+1) dimensions, living at finite density and possessing nontrivial topological charges and non-Abelian internal symmetries (both local and global). With suitable types of Ansätze, one can construct infinite-dimensional families of analytic solutions with nonvanishing topological charges (representing the baryonic number) labeled by both two integer numbers and by free scalar fields in (1+1) dimensions. These exact configurations represent (3+1)-dimensional topological solitons hosting (1+1)-dimensional chiral modes localized at the energy density peaks. First, we analyze the Yang-Mills-Higgs model, in which the fields depend on all the space-time coordinates (to keep alive the topological Chern-Simons charge), but in such a way to reduce the equations system to the field equations of two-dimensional free massless chiral scalar fields. Then, we move to the nonlinear sigma model, showing that a suitable Ansatz reduces the field equations to the one of a two-dimensional free massless scalar field. Then, we discuss the Skyrme model concluding that the inclusion of the Skyrme term gives rise to a chiral two-dimensional free massless scalar field (instead of a free massless field in two dimensions as in the nonlinear sigma model) describing analytically spatially modulated hadronic layers and tubes. The comparison of the present approach both with the instanton-dyon liquid approach and with lattice QCD is shortly outlined.

Original languageEnglish
Article number105016
JournalPhysical Review D
Volume106
Issue number10
DOIs
StatePublished - 2022

Bibliographical note

Funding Information:
F. C. has been funded by Fondecyt Grant No. 1200022. M. L. is funded by FONDECYT postdoctoral Grant No. 3190873. A. V. is funded by FONDECYT postdoctoral Grant No. 3200884. The Centro de Estudios Científicos (CECs) is funded by the Chilean Government through the Centers of Excellence Base Financing Program of ANID.

Publisher Copyright:
© 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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