Wrapped branes and confined momentum Original Research Article

We present string-like soliton solutions of three-dimensional gravity, coupled to a compact scalar field x11 and Kaluza-Klein reduced on a circle. These solitons carry fractional magnetic flux with respect to the Kaluza-Klein gauge field. Summing over such “Kaluza-Klein flux tubes” is shown to imply summing over a subclass of three-dimensional topologies (Seifert manifolds). It is also argued to imply an area law for the Wilson loop of the Kaluza-Klein gauge field; the confined charge is nothing but Kaluza-Klein momentum. Applied to the membrane of M-theory, this is interpreted in terms of “wrapping” of the M-brane around its eleventh embedding dimension x11.