Toward unification of topological solitons and instantons
by
Muneto Nitta(Keio University)
→
Europe/Stockholm
122:026
122:026
Description
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].
