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.
Highlights
A gauge potential—as opposed to a field strength—is not merely a mathematical object, but rather a physical quantity, as manifested by the Aharonov-Bohm (AB) effect [1], which is a quantummechanical effect occurring when a charged particle scatters from a solenoid with nonzero magnetic flux inside
The AB effect is studied in various areas of physics, from particle physics, quantum field theory, and string theory to cosmology
We study the behavior of the Alice string when the doublet fields develop a vacuum expectation value (VEV)
Summary
A gauge potential—as opposed to a (magnetic or electric) field strength—is not merely a mathematical object, but rather a physical quantity, as manifested by the Aharonov-Bohm (AB) effect [1], which is a quantummechanical effect occurring when a charged particle scatters from a solenoid with nonzero magnetic flux inside. To illustrate our mechanism we discuss a simpler example of an Alice string in a Uð1Þ × SUð2Þ gauge theory coupled with complex triplet scalar fields. We introduce doublet scalar fields charged or chargeless under the Uð1Þ group, which receive nontrivial AB phases in the presence of an Alice string. In the Appendix we give a detailed explanation of our numerical method
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