  Bound states in the continuum (BICs) defy conventional wisdom that assumes a
spectral separation between propagating waves, that carry energy away, and
spatially localized waves corresponding to discrete frequencies. They can be
described as resonance states with infinite lifetime, i.e., leaky modes with
zero leakage. The advent of metamaterials and nanophotonics allowed the
creation of BICs in a variety of systems. Mainly, BICs have been realized by
destructive interference between outgoing resonant modes or exploiting
engineered global symmetries that enforce the decoupling of a
symmetry-incompatible bound mode from the surrounding radiation modes. Here, we
introduce theoretically BICs relying on a different mechanism, namely local
symmetries that enforce a field concentration on a part of a complex system
without implying any global symmetry. We experimentally implement such BICs
using microwaves in a compact one-dimensional photonic network and show that
they emerge from the annihilation of two topological singularities, a zero and
a pole, of the measured scattering matrix. Our alternative for achieving BICs
in complex wave systems may be useful for applications like sensing, lasing,
and enhancement of nonlinear interactions that require high-$Q$ modes.
