Quantum Holonomies from Spectral Networks and Framed BPS States View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-04

AUTHORS

Maxime Gabella

ABSTRACT

We propose a method for determining the spins of BPS states supported on line defects in 4d N=2 theories of class S. Via the 2d–4d correspondence, this translates to the construction of quantum holonomies on a punctured Riemann surface C. Our approach combines the technology of spectral networks, which decomposes flat GL(K,C)-connections on C in terms of flat abelian connections on a K-fold cover of C, and the skein algebra in the 3-manifold C×[0,1], which expresses the representation theory of the quantum group Uq(glK). With any path on C, the quantum holonomy associates a positive Laurent polynomial in the quantized Fock–Goncharov coordinates of higher Teichmüller space. This confirms various positivity conjectures in physics and mathematics. More... »

PAGES

563-598

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00220-016-2729-1

DOI

http://dx.doi.org/10.1007/s00220-016-2729-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1010215333


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