Communications in Mathematical Physics

, Volume 358, Issue 3, pp 863–894 | Cite as

BPS/CFT Correspondence III: Gauge Origami Partition Function and qq-Characters

  • Nikita Nekrasov


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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© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Simons Center for Geometry and PhysicsStony Brook UniversityStony BrookUSA
  2. 2.Kharkevich Institute for Information Transmission ProblemsMoscowRussia

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