Toward unification of topological solitons and instantons
OKC/Nordita High-Energy Physics Theory seminar
Friday 17 January 2014
to 13:50 at
Muneto Nitta (UNUSUAL DAY AND TIME) (Keio University)
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  while Skyrmions become lumps when trapped into a domain wall . These relations can be promoted to higher dimensions . Yang-Mills instanton particles become sine-Gordon kinks when trapped inside a monopole string in d=4+1 .
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 , while a spherical domain wall with S2 moduli twisted is a Skyrmion in the Skyrme model in d=3+1 . 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 . 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 .