2016/11/01 by Pietro Longhi, Longhi, Pietro · 3 citations
Mathematics · Medicine · Pharmacology, Toxicology and Pharmaceutics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Fluorine in Organic Chemistry #High Energy Physics - Theory (hep-th) #IgG4-Related and Inflammatory Diseases #Nonlinear Waves and Solitons #hep-th #math.AG
paper · pdf · doi:10.48550/arxiv.1611.00150
A software for graph combinatorics is included with submission files; v2 a correction to section 4.8
openalex publication_date 2016/11/01 · arxiv created 2017/06/01 · arxiv updated 2017/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. The topology of the graph, together with a notion of framing, encode equations that determine the monodromy. We develop an algorithmic technique for solving the equations, and compute the monodromy in several examples. The graph manifestly encodes the symmetries of the monodromy, providing some support for conjectural relations to specializations of the superconformal index. For A1-type theories, the graphs encoding the monodromy are "dessins d'enfants" on C, the corresponding Strebel differentials coincide with the quadratic differentials that characterize the Seiberg-Witten curve.