Pilot wave theory says that there exist waves in 3D space which carry particles. This explains, say, the double slit experiment.
But this does not explain the behavior of identical particles. According to standard QM, a system of two identical particles will have quantum interference. But this interference does not take place in the real world 3D space, but rather in an abstract space. The wavefunction of two identical particles looks like $\psi (x_1,x_2)$. But the points $(x_1,x_2)$ live in an abstract space, as in, $(x_1,x_2)$ is not to be identified with a location in the real world 3D space. Rather, it is to be identified with a configuration of the system.
So, since the waves in pilot wave theory live in the real world space, how can it explain the wave-like interference in abstract spaces?