It is well known that the Yang-Mills instanton equations in R4 may be reduced to the static monopole equation in R3, by requiring the gauge potential to be independent of one coordinate. Furthermore, the static monopole solution may be obtained from an instanton chain in the limit in which the number of instantons becomes infinite. In this letter we point out that there is a simple lower dimensional analogue of this result. By requiring the gauge potential of the CP1 s-model in R2 to be independent of one coordinate, the static sine-Gordon equation in R may be obtained. Furthermore, the sine-Gordon soliton solution may be constructed from a CP1 instanton chain in the limit in which the instanton number becomes infinite.
|Number of pages||3|
|Journal||Physics Letters B|
|Publication status||Published - 1993|