Wrapped Branes and Confined Momentum

TL;DR

This paper explores string-like solitons in three-dimensional gravity with a scalar field, revealing how summing over flux tubes leads to topological implications and a confinement mechanism for Kaluza-Klein momentum, interpreted as membrane wrapping in M-theory.

Contribution

It introduces new soliton solutions in 3D gravity coupled to a scalar, linking flux tube summation to topology and confinement, with implications for M-theory brane dynamics.

Findings

Flux tubes imply summing over Seifert manifolds.

Wilson loop exhibits an area law indicating confinement.

Kaluza-Klein momentum is confined as membrane wrapping.

Abstract

We present string-like soliton solutions of three-dimensional gravity, coupled to a compact scalar field $x^{11}$ 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 shown 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 as ``dynamical wrapping'' of the M-brane around its eleventh embedding dimension $x^{11}$.