Magnetically charged calorons with non-trivial holonomy

Journal of High Energy Physics, Jun 2018

Abstract Instantons in pure Yang-Mills theories on partially periodic space \( {\mathrm{\mathbb{R}}}^3\times {S}^1 \) are usually called calorons. The background periodicity brings on characteristic features of calorons such as non-trivial holonomy, which plays an essential role for confinement/deconfinement transition in pure Yang-Mills gauge theory. For the case of gauge group SU(2), calorons can be interpreted as composite objects of two constituent “monopoles” with opposite magnetic charges. There are often the cases that the two monopole charges are unbalanced so that the calorons possess net magnetic charge in R3. In this paper, we consider several mechanism how such net magnetic charges appear for certain types of calorons through the ADHM/Nahm construction with explicit examples. In particular, we construct analytically the gauge configuration of the (2, 1)-caloron with U(1)-symmetry, which has intrinsically magnetic charge.

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Magnetically charged calorons with non-trivial holonomy

Journal of High Energy Physics June 2018, 2018:24 | Cite as Magnetically charged calorons with non-trivial holonomy AuthorsAuthors and affiliations Takumi KatoAtsushi NakamulaKoki Takesue Open Access Regular Article - Theoretical Physics First Online: 05 June 2018 Received: 14 April 2018 Accepted: 03 June 2018 1 Shares 50 Downloads Abstract Instantons in pure Yang-Mills theories on partially periodic space \( {\mathrm{\mathbb{R}}}^3\times {S}^1 \) are usually called calorons. The background periodicity brings on characteristic features of calorons such as non-trivial holonomy, which plays an essential role for confinement/deconfinement transition in pure Yang-Mills gauge theory. For the case of gauge group SU(2), calorons can be interpreted as composite objects of two constituent “monopoles” with opposite magnetic charges. There are often the cases that the two monopole charges are unbalanced so that the calorons possess net magnetic charge in R3. In this paper, we consider several mechanism how such net magnetic charges appear for certain types of calorons through the ADHM/Nahm construction with explicit examples. In particular, we construct analytically the gauge configuration of the (2, 1)-caloron with U(1)-symmetry, which has intrinsically magnetic charge. Keywords Solitons Monopoles and Instantons Integrable Field Theories Wilson ’t Hooft and Polyakov loops  ArXiv ePrint: 1804.03268 Download to read the full article text Notes Open Access This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. References [1] D.J. Gross, R.D. Pisarski and L.G. Yaffe, QCD and Instantons at Finite Temperature, Rev. Mod. Phys. 53 (1981) 43 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [2] M. Shifman and M. Ünsal, Confinement in Yang-Mills: Elements of a Big Picture, Nucl. 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Takumi Kato, Atsushi Nakamula, Koki Takesue. Magnetically charged calorons with non-trivial holonomy, Journal of High Energy Physics, 2018, 24, DOI: 10.1007/JHEP06(2018)024