Topological Dirac and Weyl semimetals have an energy spectrum that hosts Weyl nodes appearing in pairs of opposite chirality. Topological stability is ensured when the nodes are separated in momentum space and unique spectral and transport properties follow. In this work, we study the effect of a spacedependent Weyl node separation, which we interpret as an emergent background axial-vector potential, on the electromagnetic response and the energy spectrum of Weyl and Dirac semimetals. This situation can arise in the solid state either from inhomogeneous strain or nonuniform magnetization and can also be engineered in cold atomic systems. Using a semiclassical approach, we show that the resulting axial magnetic field B5is observable through an enhancement of the conductivity as s ~ B25due to an underlying chiral pseudomagnetic effect. We then use two lattice models to analyze the effect of B5on the spectral properties of topological semimetals.We describe the emergent pseudo-Landau-level structure for different spatial profiles of B5, revealing that (i) the celebrated surface states ofWeyl semimetals, the Fermi arcs, can be reinterpreted as n = 0 pseudo-Landau levels resulting from a B5confined to the surface, (ii) as a consequence of position-momentum locking, a bulk B5creates pseudo-Landau levels interpolating in real space between Fermi arcs at opposite surfaces, (iii) there are equilibrium bound currents proportional to B5that average to zero over the sample, which are the analogs of bound currents in magnetic materials.We conclude by discussing how our findings can be probed experimentally.