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Toward unification of topological solitons and instantons
  OKC/Nordita High-Energy Physics Theory seminar

Friday 17 January 2014
from 12:50 to 13:50
at 122:026
Speaker : Muneto Nitta (UNUSUAL DAY AND TIME) (Keio University)
Abstract : I’ll discuss relation between topological solitons and instantons in diverse dimensions. It has been known in supersymmetric gauge theories that when Yang-Mills instantons or magnetic monopoles are trapped into a vortex, they become lumps or kinks, respectively, in the vortex effective theory. Instantons become Skyrmions when trapped into a domain wall. First I’ll discuss generalizations of solitons trapped into a host soliton; Lumps or vortices become sine-Gordon kinks when trapped into a domain wall [1] while Skyrmions become lumps when trapped into a domain wall [2]. These relations can be promoted to higher dimensions [3]. Yang-Mills instanton particles become sine-Gordon kinks when trapped inside a monopole string in d=4+1 [4]. Next, I’ll discuss a compactification of the world-volume of host solitons. A closed domain wall line with S1 modulus twisted are lumps in a baby Skyrme model in d=2+1 [6], while a spherical domain wall with S2 moduli twisted is a Skyrmion in the Skyrme model in d=3+1 [11]. A closed monopole string, closed vortex sheet and closed domain wall with S1, S2 and S3 moduli twisted are all Yang-Mills instantons in Yang-Mills Higgs theory in d=4+1 [5]. A toroidal domain wall with S1 moduli twisted along two cycles are Hophions (knot solitons) in d=3+1 [7,8]. When one spatial direction is compactified as R2,1 x S1, a twisted lump string winding around the circle are Hopfions [9].

[1] Phys.Rev.D86 (2012) 125004 [arXiv:1207.6958]
[2] Phys.Rev.D87 (2013) 025013 [arXiv:1210.2233]
[3] Nucl.Phys.B872 (2013) 62–71[arXiv:1211.4916]
[4] Phys.Rev.D87 (2013) 066008 [arXiv:1301.3268]
[5] arXiv:1311.2718
With Michikazu Kobayashi (Kyoto Univ)
[6] Phys.Rev.D87 (2013) 085003 [arXiv:1302.0989]
[7] arXiv:1304.4737
[8] Phys.Lett. B728 (2014) 314-318 [arXiv:1304.6021]
[9] Nucl.Phys.B876 (2013) 605-618 [arXiv:1305.7417]
[10] Phys.Rev. D87 (2013) 125013 [arXiv:1307.0242 ]
With Sven Bjarke Gudnason (NORDITA)
[11] Phys.Rev.D (2014) (to appear) [arXiv:1311.4454]

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