### Abstract

A possible electric-magnetic duality suggests that the confinement of non-Abelian electric charges manifests itself as a perturbative quantum effect for the dual magnetic charges. Motivated by this possibility, we study vacuum fluctuations around a non-Abelian monopole-antimonopole pair treated as point objects with charges g=±n/2 (n=1,2,...), and placed on the antipodes of a three sphere of radius R. We explicitly find all the fluctuation modes by linearizing and solving the Yang-Mills equations about this background field on a three sphere. We recover, generalize, and extend earlier results, including those on the stability analysis of non-Abelian magnetic monopoles. We find that for g ≥ 1 monopoles there is an unstable mode that tends to squeeze magnetic flux in the angular directions. We sum the vacuum energy contributions of the fluctuation modes for the g=1/2 case and find oscillatory dependence on the cutoff scale. Subject to certain assumptions, we find that the contribution of the fluctuation modes to the quantum zero-point energy grows as ∼-R-2/3 and hence decays more slowly than the classical -R-1 Coulomb potential for large R. However, the growth of the zero-point energy does not agree with the linear growth expected if the monopoles are confined.

Original language | English (US) |
---|---|

Article number | 105013 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 76 |

Issue number | 10 |

DOIs | |

State | Published - Nov 15 2007 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematical Physics

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*76*(10), [105013]. https://doi.org/10.1103/PhysRevD.76.105013

**Quantized non-Abelian monopoles on S3.** / Maor, Irit; Mathur, Harsh; Vachaspati, Tanmay.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 76, no. 10, 105013. https://doi.org/10.1103/PhysRevD.76.105013

}

TY - JOUR

T1 - Quantized non-Abelian monopoles on S3

AU - Maor, Irit

AU - Mathur, Harsh

AU - Vachaspati, Tanmay

PY - 2007/11/15

Y1 - 2007/11/15

N2 - A possible electric-magnetic duality suggests that the confinement of non-Abelian electric charges manifests itself as a perturbative quantum effect for the dual magnetic charges. Motivated by this possibility, we study vacuum fluctuations around a non-Abelian monopole-antimonopole pair treated as point objects with charges g=±n/2 (n=1,2,...), and placed on the antipodes of a three sphere of radius R. We explicitly find all the fluctuation modes by linearizing and solving the Yang-Mills equations about this background field on a three sphere. We recover, generalize, and extend earlier results, including those on the stability analysis of non-Abelian magnetic monopoles. We find that for g ≥ 1 monopoles there is an unstable mode that tends to squeeze magnetic flux in the angular directions. We sum the vacuum energy contributions of the fluctuation modes for the g=1/2 case and find oscillatory dependence on the cutoff scale. Subject to certain assumptions, we find that the contribution of the fluctuation modes to the quantum zero-point energy grows as ∼-R-2/3 and hence decays more slowly than the classical -R-1 Coulomb potential for large R. However, the growth of the zero-point energy does not agree with the linear growth expected if the monopoles are confined.

AB - A possible electric-magnetic duality suggests that the confinement of non-Abelian electric charges manifests itself as a perturbative quantum effect for the dual magnetic charges. Motivated by this possibility, we study vacuum fluctuations around a non-Abelian monopole-antimonopole pair treated as point objects with charges g=±n/2 (n=1,2,...), and placed on the antipodes of a three sphere of radius R. We explicitly find all the fluctuation modes by linearizing and solving the Yang-Mills equations about this background field on a three sphere. We recover, generalize, and extend earlier results, including those on the stability analysis of non-Abelian magnetic monopoles. We find that for g ≥ 1 monopoles there is an unstable mode that tends to squeeze magnetic flux in the angular directions. We sum the vacuum energy contributions of the fluctuation modes for the g=1/2 case and find oscillatory dependence on the cutoff scale. Subject to certain assumptions, we find that the contribution of the fluctuation modes to the quantum zero-point energy grows as ∼-R-2/3 and hence decays more slowly than the classical -R-1 Coulomb potential for large R. However, the growth of the zero-point energy does not agree with the linear growth expected if the monopoles are confined.

UR - http://www.scopus.com/inward/record.url?scp=36249008593&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36249008593&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.76.105013

DO - 10.1103/PhysRevD.76.105013

M3 - Article

VL - 76

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 10

M1 - 105013

ER -