  The space of solutions to the Hitchin equations on the dual torus with
punctures determines the Higgs branch of certain impurity theories. An
alternative description of this Higgs branch is provided, in terms of the
proper deformation of Hitchin system with deformation parameter given by a
$B$-field. For the dual torus minus the singular points we construct explicit
solutions to the B-deformed Hitchin equations by reducing them to principal
chiral model equations and then using deformation quantization methods.
