Monopole-fermion scattering in a chiral gauge theory

The scattering of electrically charged fermions on magnetic monopole leads to the Callan-Rubakov effect. We discuss some aspects of this problem for Abelian gauge theories with chiral fermions in a Dirac monopole background. In some cases, it is possible to embed the theory in a non-Abelian gauge theory where the monopole is regularized as a ’t Hooft-Polyakov monopole. One theory of this kind is the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mi>N</a:mi><a:mo stretchy="false">)</a:mo></a:mrow></a:math> chiral gauge theory with fermions in the representation <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mo>□</e:mo><e:mspace depth="0.0ex" height="0.0ex" width="-4pt"/><e:mo>□</e:mo><e:mo>⊕</e:mo></e:mrow></e:math> <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline" mathsize="7pt"><j:mover><j:mtable frame="solid" rowlines="solid" rowspacing="-1pt" align="bottom"><j:mtr><j:mtd><j:mi> </j:mi></j:mtd></j:mtr><j:mtr><j:mtd><j:mi> </j:mi></j:mtd></j:mtr></j:mtable><j:mo mathsize="150%">¯</j:mo></j:mover></j:math><r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi> </r:mi><r:mo>⊕</r:mo><r:mi> </r:mi><r:mn>8</r:mn><r:mi> </r:mi><r:mo>×</r:mo><r:mi> </r:mi><r:mover><r:mrow><r:mi>□</r:mi></r:mrow><r:mrow><r:mo>¯</r:mo></r:mrow></r:mover></r:math>, also called the “<t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>ψ</t:mi><t:mi>χ</t:mi><t:mi>η</t:mi></t:math>” model, with an extra adjoint scalar that induces the abelianization of the gauge group. We examine this model in detail and provide a possible solution for the condensates around the monopole, the symmetry preserving boundary conditions, and discuss the particle scattering problem. Published by the American Physical Society 2024