Spectral Networks

We introduce new geometric objects called spectral networks. Spectral networks are networks of trajectories on Riemann surfaces obeying certain local rules. Spectral networks arise naturally in four-dimensional $${\mathcal{N} = 2}$$ theories coupled to surface defects, particularly the theories of class S. In these theories, spectral networks provide a useful tool for the computation of BPS degeneracies; the network directly determines the …