Quantized non-Abelian monopoles on S3

Irit Maor, Harsh Mathur, Tanmay Vachaspati

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish (US)
Article number105013
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume76
Issue number10
DOIs
StatePublished - Nov 15 2007
Externally publishedYes

Fingerprint

Monopole
monopoles
Fluctuations
Zero Point
zero point energy
Charge
Vacuum
Energy
antipodes
Magnetic Monopoles
Antipode
Yang-Mills Equation
vacuum
Coulomb Potential
magnetic monopoles
Quantum Effects
Coulomb potential
electric charge
magnetic flux
Stability Analysis

ASJC Scopus subject areas

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

Cite this

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

In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 76, No. 10, 105013, 15.11.2007.

Research output: Contribution to journalArticle

@article{28b6244b3c704fad8c32629b6143d79b,
title = "Quantized non-Abelian monopoles on S3",
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.",
author = "Irit Maor and Harsh Mathur and Tanmay Vachaspati",
year = "2007",
month = "11",
day = "15",
doi = "10.1103/PhysRevD.76.105013",
language = "English (US)",
volume = "76",
journal = "Physical review D: Particles and fields",
issn = "1550-7998",
publisher = "American Institute of Physics Publising LLC",
number = "10",

}

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 -