Bands and gaps in Nekrasov partition function

TL;DR

This paper explores the structure of Nekrasov partition functions, revealing bands and gaps in the spectrum of related quantum systems, and connects these findings to phenomena in Liouville theory, AdS3 gravity, and monopole production.

Contribution

It provides a local 2d description of gaps in the spectrum of twisted superpotentials and discusses wall-crossing, linking quantum field theory, classical Liouville theory, and gravity.

Findings

Identification of spectral gaps in twisted superpotentials

Connection between wall-crossing phenomena and classical Liouville theory

Interpretation of band structures in terms of monopole-pair production

Abstract

We discuss the effective twisted superpotentials of 2d $\mathcal{N}=(2,2)$ theories arising upon the reduction of 4d $\mathcal{N}=2$ gauge theories on the $\Omega$-deformed cigar-like geometry. We explain field-theoretic origins of the gaps in the spectrum in the corresponding quantum mechanical (QM) systems. We find local 2d descriptions of the physics near these gaps by resumming the non-perturbative part of the twisted superpotential and discuss arising wall-crossing phenomena. The interpretation of the associated phenomena in the classical Liouville theory and in the scattering of two heavy states in $AdS_3$ gravity is suggested. Some comments concerning a possible interpretation of the band structure in QM in terms of the Schwinger monopole-pair production in 4d are presented.