Abstract
We study the topology of Nielsen–Olesen's local field theory ofsingle dual string. Based on the Chern–Simons field theory in three dimensons,we find many strings that can form world sheets in four dimensions. Thesestrings have important relation to the zero point of the complex scalarfield. These world sheets of strings can be expressed by the topologicalinvariant number, Hopf index, and Brower degree. Nambu–Goto's action isobtained from the Nielsen's action definitely by using ϕ-mapping theory.
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