Aharonov-Bohm defects

Abstract

We discuss what happens when a field that receives an Aharonov-Bohm (AB) phase develops a vacuum expectation value (VEV), using the example of an Alice string in a $U(1)\ifmmode\times\else\texttimes\fi{}SU(2)$ gauge theory coupled with complex triplet scalar fields. We introduce scalar fields belonging to the doublet representation of $SU(2)$, charged or chargeless under the $U(1)$ gauge symmetry, that receives an AB phase around the Alice string. When the doublet develops a VEV, the Alice string becomes a global string in the absence of the interaction depending on the relative phase between the doublet and triplet, while in the presence of such an interaction the Alice string is confined by a soliton or domain wall, and therefore the spatial rotation around the string is spontaneously broken. We call such an object induced by an AB phase an ``AB defect,'' and argue that such a phenomenon is ubiquitous in various systems.