  We introduce a continuous one-dimensional non-Hermitian matrix gauge
potential and study its effect on dynamics of a two-component field. The model
is emulated by a system of evanescently coupled nonlinear waveguides with
distributed gain and losses. The considered gauge fields lead to a variety of
unusual physical phenomena in both linear and nonlinear regimes. In the linear
regime, the field may undergo superexponential convective amplification. A
total power of an input Gaussian beam may exhibit a finite-distance blowup,
which manifests itself in absolute delocalization of the beam at a finite
propagation distance, where the amplitude of the field remains finite. The
defocusing Kerr nonlinearity initially enhances superexponential amplification,
while at larger distances it suppresses the growth of the total power. The
focusing nonlinearity at small distances slows down the power growth and
eventually leads to the development of the modulational instability. Complex
periodic gauge fields lead to the formation of families of stable fundamental
and dipole solitons.
