I don't know much about Instantons, and looking through the Wiki page it seems like one must have a lot of knowledge about QFT to understand them. However recently I've encountered a statement (which I cannot refer to or extract more information) that instantons are "-1 dimensional" objects in the context of string theory.

The explanation is that if a 0-dimensional object (pointlike-particle) creates 1D worldline the spacetime, the 1-dimensional object (string) creates 2D worldsheet in the spacetime, instanton can create 0D-event(s) in spacetime.

  • How can it be a -1 dimensional object? Can you explain it in more details?

  • Are there any materials about instantons (which deals with some simple technical aspects) you can present?


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 count spatial dimensions; intuitively because, except for an single instant of time, it is not there.

Concerning resource recommendations for instantons:

  1. S. Coleman, Aspects of symmetry, Chapter 7. (Note that Coleman calls solitons for lumps.)

  2. G. 't Hooft and F. Bruckmann, Monopoles, Instantons and Confinement, arXiv:hep-th/0010225.

  3. Many QFT textbooks has a section on instantons, e.g., S. Weinberg, QFT2, Section 23.5; L.H. Ryder, QFT, Section 10.5.

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