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

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.

v2. 26 pages, paper 3 in the series of 5, minor typos; v3. 33 pages, notations streamlined, presentation (hopefully) improved, refs added

References in corpus (1)

• BPS/CFT correspondence II: Instantons at crossroads, Moduli and Compactness Theorem

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