Topological Classification of Symmetry Breaking and Vacuum Degeneracy

Simon-Raphael Fischer; Mehran Jalali Farahani; Hyungrok Kim; Christian Saemann

Topological Classification of Symmetry Breaking and Vacuum Degeneracy

Simon-Raphael Fischer, Mehran Jalali Farahani, Hyungrok Kim, Christian Saemann

Research output: Working paper › Preprint

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Abstract

We argue that a general system of scalar fields and gauge fields manifesting vacuum degeneracy induces a principal groupoid bundle over spacetime and that the pattern of spontaneous symmetry breaking and the Higgs mechanism are encoded by the singular foliation canonically induced on the moduli space of scalar vacuum expectation values by the Lie groupoid structure. Recent mathematical results in the classification of singular foliations then provide a qualitative classification of the possible patterns of vacuum degeneracy.

Original language	English
Publisher	arXiv
Publication status	Published - 25 Jun 2024

Keywords

hep-th
math-ph
math.DG
math.MP
53C12 (Primary) 70S15, 81T13, 57R30 (Secondary)

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abstract = "We argue that a general system of scalar fields and gauge fields manifesting vacuum degeneracy induces a principal groupoid bundle over spacetime and that the pattern of spontaneous symmetry breaking and the Higgs mechanism are encoded by the singular foliation canonically induced on the moduli space of scalar vacuum expectation values by the Lie groupoid structure. Recent mathematical results in the classification of singular foliations then provide a qualitative classification of the possible patterns of vacuum degeneracy.",

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N2 - We argue that a general system of scalar fields and gauge fields manifesting vacuum degeneracy induces a principal groupoid bundle over spacetime and that the pattern of spontaneous symmetry breaking and the Higgs mechanism are encoded by the singular foliation canonically induced on the moduli space of scalar vacuum expectation values by the Lie groupoid structure. Recent mathematical results in the classification of singular foliations then provide a qualitative classification of the possible patterns of vacuum degeneracy.

AB - We argue that a general system of scalar fields and gauge fields manifesting vacuum degeneracy induces a principal groupoid bundle over spacetime and that the pattern of spontaneous symmetry breaking and the Higgs mechanism are encoded by the singular foliation canonically induced on the moduli space of scalar vacuum expectation values by the Lie groupoid structure. Recent mathematical results in the classification of singular foliations then provide a qualitative classification of the possible patterns of vacuum degeneracy.

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KW - 53C12 (Primary) 70S15, 81T13, 57R30 (Secondary)

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BT - Topological Classification of Symmetry Breaking and Vacuum Degeneracy

PB - arXiv

ER -

Topological Classification of Symmetry Breaking and Vacuum Degeneracy

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Keywords

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