5d/6d DE instantons from trivalent gluing of web diagrams

Abstract

We propose a new prescription for computing the Nekrasov partition functions of five-dimensional theories with eight supercharges realized by gauging non-perturbative flavor symmetries of three five-dimensional superconformal field theories. The topological vertex formalism gives a way to compute the partition functions of the matter theories with flavor instanton backgrounds, and the gauging is achieved by summing over Young diagrams. We apply the prescription to calculate the Nekrasov partition functions of various five-dimensional gauge theories such as $\mathrm{SO}(2N)$ gauge theories with or without hypermultiplets in the vector representation and also pure $E_6,E_7,E_8$ gauge theories. Furthermore, the technique can be applied to computations of the Nekrasov partition functions of five-dimensional theories which arise from circle compactifications of six-dimensional minimal superconformal field theories characterized by the gauge groups $\mathrm{SU}(3),\mathrm{SO}(8),E_6,E_7,E_8$. We exemplify our method by comparing some of the obtained partition functions with known results and find perfect agreement. We also present a prescription of extending the gluing rule to the refined topological vertex.

66 pages, 28 figures; v2: typos corrected, references added and a Mathematica notebook for some checks added

References in corpus (12)

• The Refined Topological Vertex
• 6d Conformal Matter
• Surface Operator, Bubbling Calabi-Yau and AGT Relation
• Coulomb branch Hilbert series and Three Dimensional Sicilian Theories
• Refined Chern-Simons Theory and Topological String
• On certain aspects of string theory/gauge theory correspondence
• Equivalence of several descriptions for 6d SCFT
• Exact partition functions of Higgsed 5d $T_N$ theories
• 6d strings from new chiral gauge theories
• Flop Invariance of Refined Topological Vertex and Link Homologies
• Flop invariance of the topological vertex
• General instanton counting and 5d SCFT

Cited by in corpus (41)

• 6D SCFTs and Phases of 5D Theories
• Top Down Approach to 6D SCFTs
• Three dimensional canonical singularity and five dimensional N=1 SCFT
• LieART 2.0 -- A Mathematica Application for Lie Algebras and Representation Theory
• Phases of 5d SCFTs from M-/F-theory on Non-Flat Fibrations
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey
• Topological Strings on Singular Elliptic Calabi-Yau 3-folds and Minimal 6d SCFTs
• (p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters
• Revisiting the classifications of 6d SCFTs and LSTs
• Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study
• Towards Classification of 5d SCFTs: Single Gauge Node
• Rank-3 antisymmetric matter on 5-brane webs
• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
• Blowup Equations for 6d SCFTs. I
• A slow review of the AGT correspondence
• Bootstrapping BPS spectra of 5d/6d field theories
• Blowup Equations for Refined Topological Strings
• On elliptic genera of 6d string theories
• Topological vertex formalism with O5-plane
• Refined geometric transition and $qq$-characters
• 6d strings and exceptional instantons
• Quantum toroidal algebras and solvable structures in gauge/string theory
• Green-Schwarz Automorphisms and 6D SCFTs
• More on topological vertex formalism for 5-brane webs with O5-plane
• Instanton counting and O-vertex
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions
• Web Construction of ABCDEFG and Affine Quiver Gauge Theories
• Exploring the orthosymplectic zoo
• Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants
• ABCD of 't Hooft operators
• ABCD of qq-characters
• 6d/5d exceptional gauge theories from web diagrams
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Argyres-Douglas Theories, S-duality and AGT Correspondence
• S-foldings of 5d SCFTs
• $DE$-type little strings from glued brane webs
• SCFTs, Holography, and Topological Strings
• Bootstrapping ADE M-strings
• Gauge origami and quiver W-algebras IV: Pandharipande--Thomas $qq$-characters