Topologically Alice Strings and Monopoles

TL;DR

This paper establishes a topological criterion linking Alice strings to monopoles, demonstrating that certain condensed matter systems support topologically nontrivial Alice loops that can carry monopole charge.

Contribution

It introduces a topological criterion for Alice behavior, connecting it to monopoles, and applies this to various physical systems to identify topologically Alice strings and monopoles.

Findings

Topological criterion links Alice strings to monopoles.

Condensed matter systems support topologically Alice loops with monopole charge.

Twisted Alice loops can support fundamental monopole charge.

Abstract

Symmetry breaking can produce ``Alice'' strings, which alter scattered charges and carry monopole number and charge when twisted into loops. Alice behavior arises algebraically, when strings obstruct unbroken symmetries -- a fragile criterion. We give a topological criterion, compelling Alice behavior or deforming it away. Our criterion, that \pi_o(H) acts nontrivially on \pi_1(H), links topologically Alice strings to topological monopoles. We twist topologically Alice loops to form monopoles. We show that Alice strings of condensed matter systems (nematic liquid crystals, helium 3A, and related non-chiral Bose condensates and amorphous chiral superconductors) are topologically Alice, and support fundamental monopole charge when twisted into loops. Thus they might be observed indirectly, not as strings, but as loop-like point defects. We describe other models, showing Alice strings failing our topological criterion; and twisted Alice loops supporting deposited, but not fundamental, monopole number.