2017/10/12 by Lotte Hollands, Hollands, Lotte, Omar Kidwai +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Chemistry · Physics and Astronomy · #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #Molecular spectroscopy and chirality #Protein Structure and Dynamics #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.1710.04438
openalex publication_date 2017/10/12 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
In this paper we study a proposal of Nekrasov, Rosly and Shatashvili that\ndescribes the effective twisted superpotential obtained from a class S theory\ngeometrically as a generating function in terms of certain complexified\nlength-twist coordinates, and extend it to higher rank. First, we introduce a\nhigher rank analogue of Fenchel-Nielsen type spectral networks in terms of a\ngeneralized Strebel condition. We find new systems of spectral coordinates\nthrough the abelianization method and argue that they are higher rank analogues\nof the Nekrasov-Rosly-Shatashvili Darboux coordinates. Second, we give an\nexplicit parametrization of the locus of opers and determine the generating\nfunctions of this Lagrangian subvariety in terms of the higher rank Darboux\ncoordinates in some specific examples. We find that the generating functions\nindeed agree with the known effective twisted superpotentials. Last, we relate\nthe approach of Nekrasov, Rosly and Shatashvili to the approach using quantum\nperiods via the exact WKB method.\n