Gauge string in the fermion asymmetric matter

Two new effects of interaction of the gauge string with a homogeneous density of fermions are considered in a gauge model with an anomalous coupling of vector fields with fermions. First, the presence of an induced nonzero magnetic-like helicity on the straight string is demonstrated. Second, it is shown that the equation of motion of the string is modified by a nonlinear term that can be decomposed into the correction to the string tension and an additional force perpendicular to the tangent and normal vectors of the string. Static configurations are found and their stability is studied.