  We consider a two-dimensional extension of the 1D waveguide quantum
electrodynamics and investigate the nature of linear excitations in
two-dimensional arrays of qubits coupled to networks of chiral waveguides. We
show that the combined effects of chirality and long-range photon mediated
qubit-qubit interactions lead to the emergence of the two-dimensional flat
bands in the polaritonic spectrum, corresponding to slow strongly correlated
light.
