BPS/CFT Correspondence III: Gauge Origami partition function and qq-characters

TL;DR

This paper explores the gauge origami framework derived from Dp-branes on Calabi-Yau fourfolds, analyzing partition functions and qq-characters with implications for gauge theory and string theory.

Contribution

It introduces the gauge origami model for generalized gauge theories and studies its partition function's analytic properties and qq-characters in the context of toric Calabi-Yau fourfolds.

Findings

Partition function is an entire function of Coulomb moduli.

Orbifold theory defines qq-characters with and without surface defects.

Analytic properties linked to moduli space compactness.

Abstract

We study generalized gauge theories engineered by taking the low energy limit of the $Dp$ branes wrapping $X \times T^{p-3}$, with $X$ a possibly singular surface in a Calabi-Yau fourfold $Z$. For toric $Z$ and $X$ the partition function can be computed by localization, making it a statistical mechanical model, called the gauge origami. The random variables are the ensembles of Young diagrams. The building block of the gauge origami is associated with a tetrahedron, whose edges are colored by vector spaces. We show the properly normalized partition function is an entire function of the Coulomb moduli, for generic values of the $\Omega$-background parameters. The orbifold version of the theory defines the $qq$-character operators, with and without the surface defects. The analytic properties are the consequence of a relative compactness of the moduli spaces $M({\vec n}, k)$ of crossed and spiked instantons, demonstrated in arXiv:1608.07272.