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Extended Soliton Solutions in an Effective Action for $\mathrm{SU}(2)$ Yang–Mills Theory
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

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The Skyrme–Faddeev–Niemi (SFN) model which is an $O(3)$ $\sigma$ model in three dimensional space up to fourth-order in the first derivative is regarded as a low-energy effective theory of $SU(2)$ Yang–Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang–Mills theory recovers the SFN in the infrared region. However, the theory contains an additional fourth-order term which destabilizes the soliton solution. We apply the perturbative treatment to the second derivative term in order to exclude (or reduce) the ill behavior of the original action and show that the SFN model with the second derivative term possesses soliton solutions.
Keywords: topological soliton; Yang–Mills theory; second derivative field theory. 
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     author = {Nobuyuki Sawado and Noriko Shiiki and Shingo Tanaka},
     title = {Extended {Soliton} {Solutions} in an {Effective} {Action} for $\mathrm{SU}(2)$ {Yang{\textendash}Mills} {Theory}},
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}
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Nobuyuki Sawado; Noriko Shiiki; Shingo Tanaka. Extended Soliton Solutions in an Effective Action for $\mathrm{SU}(2)$ Yang–Mills Theory. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a15/

[1] Faddeev L., Niemi A., “Knots and particles”, Nature, 387 (1997), 58–61 ; arXiv:hep-th/9610193 | DOI

[2] Gladikowski J., Hellmund M., “Static solitons with nonzero hopf number”, Phys. Rev. D, 56 (1997), 5194–5199 ; arXiv:hep-th/9609035 | DOI | MR

[3] Battye R. A., Sutcliffe P. M., “Solitons, links and knots”, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 455 (1999), 4301–4331 ; arXiv:hep-th/9811077 | MR

[4] Hietarinta J., Salo P., “Faddeev–Hopf knots: dynamics of linked unknots”, Phys. Lett. B, 451 (1999), 60–67 ; arXiv:hep-th/9811053 | DOI | MR | Zbl

[5] Hietarinta J., Salo P., “Ground state in the Faddeev–Skyrme model”, Phys. Rev. D, 62 (2000), 081701, 4 pp., ages | DOI

[6] Aratyn H., Ferreira L. A., Zimerman A. H., “Toroidal solitons in (3+1)-dimensional integrable theories”, Phys. Lett. B, 456 (1999), 162–170 ; arXiv:hep-th/9902141 | DOI | MR | Zbl

[7] Babaev E., Faddeev L., Niemi A. J., “Hidden symmetry and duality in a charged two condensate Bose system”, Phys. Rev. B, 65 (2002), 100512, 4 pp., ages ; arXiv:cond-mat/0106152 | DOI

[8] Fayzullaev B. A., Musakhanov M. M., Pak D. G., Siddikov M., “Knot soliton in Weinberg–Salam model”, Phys. Lett. B, 609 (2005), 442–448 ; arXiv:hep-th/0412282 | DOI | Zbl

[9] Faddeev L., Niemi A. J., “Partially dual variables in $SU(2)$ Yang–Mills theory”, Phys. Rev. Lett., 82 (1999), 1624–1627 ; arXiv:hep-th/9807069 | DOI | MR | Zbl

[10] Langmann E., Niemi A. J., “Towards a string representation of infrared $SU(2)$ Yang–Mills theory”, Phys. Lett. B, 463 (1999), 252–256 ; arXiv:hep-th/9905147 | DOI | MR | Zbl

[11] Shabanov S. V., “An effective action for monopoles and knot solitons in Yang–Mills theory”, Phys. Lett. B, 458 (1999), 322–330 ; arXiv:hep-th/9903223 | DOI | MR | Zbl

[12] Cho Y. M., Lee H. W., Pak D. G., “Faddeev–Niemi conjecture and effective action of QCD”, Phys. Lett. B, 525 (2002), 347–354 ; arXiv:hep-th/0105198 | DOI | Zbl

[13] Gies H., “Wilsonian effective action for $SU(2)$ Yang–Mills theory with Cho–Faddeev–Niemi–Shabanov decomposition”, Phys. Rev. D, 63 (2001), 125023, 8 pp., ages ; arXiv:hep-th/0102026 | DOI

[14] Dhar A., Shankar R., Wadia S. R., “Nambu–Jona–Lasinio type effective Lagrangian. 2. Anomalies and nonlinear Lagrangian of low-energy, large $N$ QCD”, Phys. Rev. D, 31 (1985), 3256–3267 | DOI

[15] Aitchison I., Fraser C., Tudor E., Zuk J., “Failure of the derivative expansion for studying stability of the baryon as a chiral soliton”, Phys. Lett. B, 165 (1985), 162–166 | DOI

[16] Marleau L., Rivard J. F., “A generating function for all orders skyrmions”, Phys. Rev. D, 63 (2001), 036007, 7 pp., ages ; arXiv:hep-ph/0011052 | DOI

[17] Vakulenko A. F., Kapitanskii L. V., “Stability of solitons in $S^2$ in the nonlinear $\sigma$ model”, Sov. Phys. Dokl., 24:6 (1979), 433–434 | Zbl

[18] Ward R. S., “Hopf solitons on $S^3$ and $\mathbf R^3$”, Nonlinearity, 12 (1999), 241–246 ; arXiv:hep-th/9811176 | DOI | MR | Zbl

[19] Manton N., Sutcliffe P., Topological solitons, Cambridge University Press, 2004 | MR | Zbl

[20] Pais A., Uhlenbeck G. E., “On field theories with non-localized action”, Phys. Rev., 79 (1950), 145–165 | DOI | MR | Zbl

[21] Smilga A. V., “Benign versus Malicious ghosts in higher-derivative theories”, Nucl. Phys. B, 706 (2005), 598–614 ; arXiv:hep-th/0407231 | DOI | MR | Zbl

[22] Eliezer D. A., Woodard R. P., “The problem of nonlocality in string theory”, Nucl. Phys. B, 325 (1989), 389–469 | DOI | MR

[23] Jaén X., Llosa L. Morina A., “A reduction of order two for infinite order Lagrangians”, Phys. Rev. D, 34 (1986), 2302–2311 | DOI

[24] Simon J. Z., “Higher derivative Lagrangians, nonlocality, problems and solutions”, Phys. Rev. D, 41 (1990), 3720–3733 | DOI | MR

[25] Faddeev L., Niemi A. J., Wiedner U., “Glueballs, closed fluxtubes, and eta(1440)”, Phys. Rev. D, 70 (2004), 114033, 5 pp., ages ; arXiv:hep-ph/0308240 | DOI

[26] Bae W. S., Cho Y. M., Park B. S., Reinterpretation of Skyrme theory, arXiv:hep-th/0404181

[27] Kondo K.-I., “Magnetic condensation, Abelian dominance, and instability of Savvidy vacuum”, Phys. Lett. B, 600 (2004), 287–296 ; arXiv:hep-th/0410024 | DOI | MR