Wall-Crossing Invariants from Spectral Networks

Understand

A new construction of BPS monodromies for 4d ${\mathcal N}=2$ theories of class S is introduced.

• A novel feature of this construction is its manifest invariance under Kontsevich-Soibelman wall crossing, in the sense that no information on the 4d BPS spectrum is employed.
• The BPS monodromy is encoded by topological data of a finite graph, embedded into the UV curve $C$ of the theory.
• The graph arises from a degenerate limit of spectral networks, constructed at maximal intersections of walls of marginal stability in the Coulomb branch of the gauge theory.