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Wall Crossing Invariants from Spectral Networks
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2018 (English)In: Annales de l'Institute Henri Poincare. Physique theorique, ISSN 1424-0637, E-ISSN 1424-0661, Vol. 19, no 3, p. 775-842Article in journal (Refereed) Published
Abstract [en]

A new construction of BPS monodromies for 4d theories of class 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 -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.

Place, publisher, year, edition, pages
2018. Vol. 19, no 3, p. 775-842
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URN: urn:nbn:se:uu:diva-351267DOI: 10.1007/s00023-017-0635-5ISI: 000426309600005OAI: oai:DiVA.org:uu-351267DiVA, id: diva2:1216338
Available from: 2018-06-11 Created: 2018-06-11 Last updated: 2018-06-11Bibliographically approved

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Longhi, Pietro

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