Abstract
We study generalized gauge theories engineered by taking the low energy limit of the Dp branes wrapping \({X \times {\bf T}^{p-3}}\), 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 \({\underline{\rm gauge\,origami}}\). 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 \({\mathcal{M}({\vec n}, k)}\) of crossed and spiked instantons, demonstrated in “BPS/CFT correspondence II: instantons at crossroads, moduli and compactness theorem”.
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Nekrasov, N. BPS/CFT Correspondence III: Gauge Origami Partition Function and qq-Characters. Commun. Math. Phys. 358, 863–894 (2018). https://doi.org/10.1007/s00220-017-3057-9
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DOI: https://doi.org/10.1007/s00220-017-3057-9