Generalized semilocal theories and higher Hopf maps

Mark Hindmarsh; Richard Holman; Thomas W. Kephart; Tanmay Vachaspati

doi:10.1016/0550-3213(93)90597-I

Generalized semilocal theories and higher Hopf maps

Mark Hindmarsh, Richard Holman, Thomas W. Kephart, Tanmay Vachaspati

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14 Scopus citations

Abstract

In semilocal theories, the vacuum manifold is fibered in a non-trivial way the action of the gauge group. Here we generalize the original semilocal theory (which was based on the Hopf bundle S^3S1 → S²) to realize the next Hopf bundle S^3S3 → S⁴, and its extensions S²ⁿ⁺¹ → ^S3 S⁴, and its extensions S^2n+12n+1S3 → HPⁿ. The semilocal defects in this class of theories are classified by π₃S³), and are interpreted as constrained instantons or generalized sphaleron configurations. We fail to find a field theoretic realization of the final Hopf bundle S^15S7 → S⁸, but are able to construct other semilocal spaces realizing Stiefel bundles over grassmannian spaces.

Original language	English (US)
Pages (from-to)	794-804
Number of pages	11
Journal	Nuclear Physics, Section B
Volume	404
Issue number	3
DOIs	https://doi.org/10.1016/0550-3213(93)90597-I
State	Published - Sep 6 1993
Externally published	Yes

ASJC Scopus subject areas

Nuclear and High Energy Physics

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@article{1b1534b520ff468f80208dd43bf75642,

title = "Generalized semilocal theories and higher Hopf maps",

abstract = "In semilocal theories, the vacuum manifold is fibered in a non-trivial way the action of the gauge group. Here we generalize the original semilocal theory (which was based on the Hopf bundle S3S1 → S2) to realize the next Hopf bundle S3S3 → S4, and its extensions S2n+1 → S3 S4, and its extensions S2n+12n+1S3 → HPn. The semilocal defects in this class of theories are classified by π3S3), and are interpreted as constrained instantons or generalized sphaleron configurations. We fail to find a field theoretic realization of the final Hopf bundle S15S7 → S8, but are able to construct other semilocal spaces realizing Stiefel bundles over grassmannian spaces.",

author = "Mark Hindmarsh and Richard Holman and Kephart, {Thomas W.} and Tanmay Vachaspati",

note = "Funding Information: This research was supported in part by the National Science Foundation under grant No. PHY89-04035. R.H. was supported in part by DOE contract DE-FGO2-91ER40682. T.W.K. was supported by the DOE (grant DE-FGO5-85ER40266). M.H. wishes to thank the Theoretical Division at the Los Alamos National Laboratory and the Theoretical Astrophysics group at Fermilab for their hospitality while this work was being completed.",

year = "1993",

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doi = "10.1016/0550-3213(93)90597-I",

language = "English (US)",

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T1 - Generalized semilocal theories and higher Hopf maps

AU - Hindmarsh, Mark

AU - Holman, Richard

AU - Kephart, Thomas W.

AU - Vachaspati, Tanmay

N1 - Funding Information: This research was supported in part by the National Science Foundation under grant No. PHY89-04035. R.H. was supported in part by DOE contract DE-FGO2-91ER40682. T.W.K. was supported by the DOE (grant DE-FGO5-85ER40266). M.H. wishes to thank the Theoretical Division at the Los Alamos National Laboratory and the Theoretical Astrophysics group at Fermilab for their hospitality while this work was being completed.

PY - 1993/9/6

Y1 - 1993/9/6

N2 - In semilocal theories, the vacuum manifold is fibered in a non-trivial way the action of the gauge group. Here we generalize the original semilocal theory (which was based on the Hopf bundle S3S1 → S2) to realize the next Hopf bundle S3S3 → S4, and its extensions S2n+1 → S3 S4, and its extensions S2n+12n+1S3 → HPn. The semilocal defects in this class of theories are classified by π3S3), and are interpreted as constrained instantons or generalized sphaleron configurations. We fail to find a field theoretic realization of the final Hopf bundle S15S7 → S8, but are able to construct other semilocal spaces realizing Stiefel bundles over grassmannian spaces.

AB - In semilocal theories, the vacuum manifold is fibered in a non-trivial way the action of the gauge group. Here we generalize the original semilocal theory (which was based on the Hopf bundle S3S1 → S2) to realize the next Hopf bundle S3S3 → S4, and its extensions S2n+1 → S3 S4, and its extensions S2n+12n+1S3 → HPn. The semilocal defects in this class of theories are classified by π3S3), and are interpreted as constrained instantons or generalized sphaleron configurations. We fail to find a field theoretic realization of the final Hopf bundle S15S7 → S8, but are able to construct other semilocal spaces realizing Stiefel bundles over grassmannian spaces.

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EP - 804

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 3

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Generalized semilocal theories and higher Hopf maps

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