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A soliton is a localized, non-dispersive solution of a nonlinear theory in Euclidean space. It certainly is a real object: you have a famous story about a certain John Russell who observed soliton-like waves made by a boat on a river (wikipedia knows everything about it!) The so-called morning glory clouds in Australia ...


Where a string carves out a $2$-dimensional world-sheet and a point particle carves out a $1$-dimensional world-line of spacetime, the instanton carves out a $0$-dimensional world-point. Counting only spatial dimensions, a string is $1$-dimensional and a point particle is $0$-dimensional. By logical extension, an instanton has dimension $-1$, if we only ...

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