A geometric recipe for twisted superpotentials

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Abstract

We give a pedagogical introduction to spectral networks and abelianization, as well as their relevance to N = 2 supersymmetric field theories in four dimensions. Motivated by a conjecture of Nekrasov-Rosly-Shatashvili, we detail a geometric recipe for computing the effective twisted superpotential for N = 2 field theories of class S as a generating function of the brane of opers, with respect to the spectral coordinates found from abelianization. We present two new examples, the simplest Argyres-Douglas theory and the pure SU(2) gauge theory, while we conjecture the E-expansion of the effective twisted superpotential for the E6 Minahan-Nemeschansky theory.
Original languageEnglish
Article number164
JournalJournal of High Energy Physics
Volume2021
Issue number12
DOIs
Publication statusPublished - 22 Dec 2021

Keywords

  • Differential and Algebraic Geometry
  • Duality in Gauge Field Theories
  • Su- persymmetric Gauge Theory

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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