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arXiv · 2109.14699

A geometric recipe for twisted superpotentials

Lotte Hollands·Philipp Rüter·Richard J. Szabo
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Abstract

We give a pedagogical introduction to spectral networks and abelianization, as well as their relevance to $\mathcal{N}=2$ 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 $\mathcal{N}=2$ field theories of class $\mathcal{S}$ 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 $\epsilon$-expansion of the effective twisted superpotential for the $E_6$ Minahan-Nemeschansky theory.

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Lotte Hollands, Philipp Rüter, Richard J. Szabo. 2021-09-29. A geometric recipe for twisted superpotentials. https://doi.org/10.1007/jhep12(2021)164

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