  Non-Hermiticity gives rise to unique topological phases without Hermitian
analogs. However, the effective field theory has yet to be established. Here,
we develop a field-theoretical description of the intrinsic non-Hermitian
topological phases. Because of the dissipative and nonequilibrium nature of
non-Hermiticity, our theory is formulated solely in terms of spatial degrees of
freedom, which contrasts with the conventional theory defined in spacetime. It
provides the universal understanding about non-Hermitian topological phenomena,
such as the unidirectional transport in one dimension and the chiral magnetic
skin effect in three dimensions. Furthermore, it systematically predicts new
physics; we illustrate this by revealing transport phenomena and skin effects
in two dimensions induced by a perpendicular spatial texture. From the
field-theoretical perspective, the non-Hermitian skin effect, which is
anomalous localization due to non-Hermiticity, is shown to be a signature of an
anomaly.
