A geometric recipe for twisted superpotentials

Abstract

Abstract We give a pedagogical introduction to spectral networks and abelianization, as well as their relevance to N $$ \mathcal{N} $$ = 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 $$ \mathcal{N} $$ = 2 field theories of class S $$ \mathcal{S} $$ 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 E 6 Minahan-Nemeschansky theory.

Keywords

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