D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants
arXiv:2304.04383 · doi:10.1007/JHEP10(2023)045
Abstract
We study the quantization of the 6d Seiberg-Witten curve for D-type minimal conformal matter theories compactified on a two-torus. The quantized 6d curve turns out to be a difference equation established via introducing codimension two and four surface defects. We show that, in the Nekrasov-Shatashvili limit, the 6d partition function with insertions of codimension two and four defects serve as the eigenfunction and eigenvalues of the difference equation, respectively. We further identify the quantum curve of D-type minimal conformal matters with an elliptic Garnier system recently studied in the integrability community. At last, as a concrete consequence of our elliptic quantum curve, we study its RG flows to obtain various quantum curves of 5d theories.
arXiv comment36+6 pages, minor updates, added refs
References in corpus (56)
- Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
- Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
- N=2 dualities
- Loop and surface operators in N=2 gauge theory and Liouville modular geometry
- On the Classification of 6D SCFTs and Generalized ADE Orbifolds
- Elliptic genera of 2d N=2 gauge theories
- Quantization of Integrable Systems and Four Dimensional Gauge Theories
- Atomic Classification of 6D SCFTs
- Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups
- 5-dim Superconformal Index with Enhanced En Global Symmetry
- Instanton counting on blowup. I. 4-dimensional pure gauge theory
- Bootstrapping the superconformal index with surface defects
- Darboux coordinates, Yang-Yang functional, and gauge theory
- On Geometric Classification of 5d SCFTs
- Quantum Geometry of Refined Topological Strings
- Defects and Quantum Seiberg-Witten Geometry
- 5d Superconformal Field Theories and Graphs
- 6D SCFTs and Phases of 5D Theories
- Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States
- Classifying 5d SCFTs via 6d SCFTs: Arbitrary rank
- Elliptic Genus of E-strings
- On Painlevé/gauge theory correspondence
- A new 5d description of 6d D-type minimal conformal matter
- instantons on type-A ALE spaces and supersymmetric field theories
- Classifying 5d SCFTs via 6d SCFTs: Rank one
- Twisted Circle Compactifications of 6d SCFTs
- E-String Theory on Riemann Surfaces
- Phases of 5d SCFTs from M-/F-theory on Non-Flat Fibrations
- 6d SCFTs, 5d Dualities and Tao Web Diagrams
- D-type Conformal Matter and SU/USp Quivers
- Compactification of 6d minimal SCFTs on Riemann surfaces
- Compactifications of 6d SCFTs with non-trivial Stiefel-Whitney classes
- Classification of 5d N=1 gauge theories
- Rank E-string on a torus with flux
- Compactifications of ADE conformal matter on a torus
- Saddle point equations in Seiberg-Witten theory
- Quantum geometry of del Pezzo surfaces in the Nekrasov-Shatashvili limit
- Equivalence of several descriptions for 6d SCFT
- Discrete theta angle from an O5-plane
- Sequences of SCFTs on generic Riemann surfaces
- Perverse coherent sheaves on blow-up. III. Blow-up formula from wall-crossing
- Refined geometric transition and -characters
- Wilson surfaces in M5-branes
- Minimal conformal matter and generalizations of the van Diejen model
- D-type fiber-base duality
- 5d/6d Wilson loops from blowups
- Spectral Theories and Topological Strings on del Pezzo Geometries
- Testing 5d-6d dualities with fractional D-branes
- Elliptic Quantum Curves of 6d SO(N) theories
- Star shaped quivers in four dimensions
- Elliptic Quantum Curves of Class
- Topological strings and Wilson loops
- Fibre-base duality of 5d KK theories
- Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
- generalization of the van Diejen model from the minimal conformal matter
- An elliptic Garnier system