2017/01/31 by Nikita Nekrasov · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Gauge theory #Geometry #Instanton #Mathematical physics #Mathematics #Moduli space #Noncommutative and Quantum Gravity Theories #Orbifold #Partition function (quantum field theory) #Physics #Pure mathematics #Quantum mechanics #Tetrahedron #Vector bundle #hep-th #math.AG #math.CO
paper · pdf · doi:10.1007/s00220-017-3057-9
v2. 26 pages, paper 3 in the series of 5, minor typos; v3. 33 pages, notations streamlined, presentation (hopefully) improved, refs added
arxiv created 2017/10/24 · openalex publication_date 2017/12/13 · arxiv updated 2018/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study generalized gauge theories engineered by taking the low energy limit of the Dp branes wrapping X × Tp-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 Ω-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( n, k) of crossed and spiked instantons, demonstrated in arXiv:1608.07272.