Abstract
We find semi-local fractional instantons of codimension four in Abelian and non-Abelian gauge theories coupled with scalar fields and the corresponding \( \mathbb{C}{P}^{N-1} \) and Grassmann sigma models at strong gauge coupling. They are 1/4 BPS states in super-symmetric theories with eight supercharges, carry fractional (half) instanton charges characterized by the fourth homotopy group π 4(G/H), and have divergent energy in infinite spaces. We construct exact solutions for the sigma models and numerical solutions for the gauge theories. Small instanton singularity in sigma models is resolved at finite gauge coupling (for the Abelian gauge theory). Instantons in Abelian and non-Abelian gauge theories have negative and positive instantons charges, respectively, which are related by the Seiberg-like duality that changes the sign of the instanton charge.
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References
N. Dorey, T.J. Hollowood, V.V. Khoze and M.P. Mattis, The Calculus of many instantons, Phys. Rept. 371 (2002) 231 [hep-th/0206063] [INSPIRE].
G.H. Derrick, Comments on nonlinear wave equations as models for elementary particles, J. Math. Phys. 5 (1964) 1252 [INSPIRE].
A. Hanany and D. Tong, Vortices, instantons and branes, JHEP 07 (2003) 037 [hep-th/0306150] [INSPIRE].
R. Auzzi, S. Bolognesi, J. Evslin, K. Konishi and A. Yung, NonAbelian superconductors: Vortices and confinement in N = 2 SQCD, Nucl. Phys. B 673 (2003) 187 [hep-th/0307287] [INSPIRE].
M. Eto, Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Moduli space of non-Abelian vortices, Phys. Rev. Lett. 96 (2006) 161601 [hep-th/0511088] [INSPIRE].
M. Eto et al., Non-Abelian Vortices of Higher Winding Numbers, Phys. Rev. D 74 (2006) 065021 [hep-th/0607070] [INSPIRE].
M. Eto, K. Hashimoto, G. Marmorini, M. Nitta, K. Ohashi and W. Vinci, Universal Reconnection of Non-Abelian Cosmic Strings, Phys. Rev. Lett. 98 (2007) 091602 [hep-th/0609214] [INSPIRE].
A. Hanany and D. Tong, Vortex strings and four-dimensional gauge dynamics, JHEP 04 (2004) 066 [hep-th/0403158] [INSPIRE].
M. Eto, Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Instantons in the Higgs phase, Phys. Rev. D 72 (2005) 025011 [hep-th/0412048] [INSPIRE].
M. Eto, Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Solitons in the Higgs phase: The Moduli matrix approach, J. Phys. A 39 (2006) R315 [hep-th/0602170] [INSPIRE].
M. Shifman and A. Yung, NonAbelian string junctions as confined monopoles, Phys. Rev. D 70 (2004) 045004 [hep-th/0403149] [INSPIRE].
T. Fujimori, M. Nitta, K. Ohta, N. Sakai and M. Yamazaki, Intersecting Solitons, Amoeba and Tropical Geometry, Phys. Rev. D 78 (2008) 105004 [arXiv:0805.1194] [INSPIRE].
M. Eto, Y. Isozumi, M. Nitta and K. Ohashi, 1/2, 1/4 and 1/8 BPS equations in SUSY Yang-Mills-Higgs systems: Field theoretical brane configurations, Nucl. Phys. B 752 (2006) 140 [hep-th/0506257] [INSPIRE].
A.M. Polyakov and A.A. Belavin, Metastable States of Two-Dimensional Isotropic Ferromagnets, JETP Lett. 22 (1975) 245 [Pisma Zh. Eksp. Teor. Fiz. 22 (1975) 503] [INSPIRE].
T. Vachaspati and A. Achucarro, Semilocal cosmic strings, Phys. Rev. D 44 (1991) 3067 [INSPIRE].
A. Achucarro and T. Vachaspati, Semilocal and electroweak strings, Phys. Rept. 327 (2000) 347 [hep-ph/9904229] [INSPIRE].
M. Hindmarsh, Existence and stability of semilocal strings, Phys. Rev. Lett. 68 (1992) 1263 [INSPIRE].
M. Shifman and A. Yung, Non-Abelian semilocal strings in N = 2 supersymmetric QCD, Phys. Rev. D 73 (2006) 125012 [hep-th/0603134] [INSPIRE].
M. Eto et al., On the moduli space of semilocal strings and lumps, Phys. Rev. D 76 (2007) 105002 [arXiv:0704.2218] [INSPIRE].
G.W. Gibbons, M.E. Ortiz, F. Ruiz Ruiz and T.M. Samols, Semilocal strings and monopoles, Nucl. Phys. B 385 (1992) 127 [hep-th/9203023] [INSPIRE].
M. Hindmarsh, Semilocal topological defects, Nucl. Phys. B 392 (1993) 461 [hep-ph/9206229] [INSPIRE].
M. Hindmarsh, R. Holman, T.W. Kephart and T. Vachaspati, Generalized semilocal theories and higher Hopf maps, Nucl. Phys. B 404 (1993) 794 [hep-th/9209088] [INSPIRE].
Y. He and H. Guo, Topological defect with nonzero Hopf invariant in Yang-Mills-Higgs model, Phys. Lett. B 739 (2014) 83 [arXiv:1405.4089] [INSPIRE].
B.J. Schroers, Bogomolny solitons in a gauged O(3) σ-model, Phys. Lett. B 356 (1995) 291 [hep-th/9506004] [INSPIRE].
B.J. Schroers, The Spectrum of Bogomol’nyi solitons in gauged linear σ-models, Nucl. Phys. B 475 (1996) 440 [hep-th/9603101] [INSPIRE].
M. Nitta and W. Vinci, Decomposing Instantons in Two Dimensions, J. Phys. A 45 (2012) 175401 [arXiv:1108.5742] [INSPIRE].
S.B. Gudnason and M. Nitta, Fractional Skyrmions and their molecules, Phys. Rev. D 91 (2015) 085040 [arXiv:1502.06596] [INSPIRE].
G.V. Dunne and M. Ünsal, Resurgence and Trans-series in Quantum Field Theory: The CP(N−1) Model, JHEP 11 (2012) 170 [arXiv:1210.2423] [INSPIRE].
G.V. Dunne and M. Ünsal, Continuity and Resurgence: towards a continuum definition of the \( \mathbb{C}\mathrm{\mathbb{P}}\left(N-1\right) \) model, Phys. Rev. D 87 (2013) 025015 [arXiv:1210.3646] [INSPIRE].
T. Misumi, M. Nitta and N. Sakai, Neutral bions in the \( \mathbb{C}{P^N}^{-1} \) model, JHEP 06 (2014) 164 [arXiv:1404.7225] [INSPIRE].
M. Eto et al., Non-Abelian vortices on cylinder: Duality between vortices and walls, Phys. Rev. D 73 (2006) 085008 [hep-th/0601181] [INSPIRE].
T. Misumi, M. Nitta and N. Sakai, Classifying bions in Grassmann σ-models and non-Abelian gauge theories by D-branes, PTEP 2015 (2015) 033B02 [arXiv:1409.3444] [INSPIRE].
M. Nitta, Fractional instantons and bions in the O(N ) model with twisted boundary conditions, JHEP 03 (2015) 108 [arXiv:1412.7681] [INSPIRE].
M. Nitta, Fractional instantons and bions in the principal chiral model on \( {\mathbb{R}}^2\times {S}^1 \) with twisted boundary conditions, JHEP 08 (2015) 063 [arXiv:1503.06336] [INSPIRE].
K. Higashijima and M. Nitta, Supersymmetric nonlinear σ-models as gauge theories, Prog. Theor. Phys. 103 (2000) 635 [hep-th/9911139] [INSPIRE].
M. Eto et al., Constructing Non-Abelian Vortices with Arbitrary Gauge Groups, Phys. Lett. B 669 (2008) 98 [arXiv:0802.1020] [INSPIRE].
M. Eto et al., Non-Abelian Vortices in SO(N ) and USp(N ) Gauge Theories, JHEP 06 (2009) 004 [arXiv:0903.4471] [INSPIRE].
M. Eto et al., Vortices and Monopoles in Mass-deformed SO and USp Gauge Theories, JHEP 12 (2011) 017 [arXiv:1108.6124] [INSPIRE].
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ArXiv ePrint: 1512.07458
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Eto, M., Nitta, M. Semilocal fractional instantons. J. High Energ. Phys. 2016, 67 (2016). https://doi.org/10.1007/JHEP03(2016)067
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DOI: https://doi.org/10.1007/JHEP03(2016)067