Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters

Abstract

We further develop the BPS/CFT correspondence between quiver W-algebras/$qq$-characters and partition functions of gauge origami. We introduce $qq$-characters associated with multi-dimensional partitions with nontrivial boundary conditions which we call Donaldson--Thomas (DT) $qq$-characters. They are operator versions of the equivariant DT vertices of toric Calabi--Yau three and four-folds. Moreover, we revisit the construction of the D8 $qq$-characters with no boundary conditions and give a quantum algebraic derivation of the sign rules of the magnificent four partition function. We also show that under the proper sign rules, the D6 and D8 $qq$-characters with no boundary conditions all commute with each other and discuss its physical interpretation.

arXiv comment66+13 pages, v2: published version

References in corpus (69)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• CFT's From Calabi-Yau Four-folds
• The Topological Vertex
• The Refined Topological Vertex
• Elliptic genera of 2d N=2 gauge theories
• Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups
• Quantum Foam and Topological Strings
• Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
• A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions
• Witten Index and Wall Crossing
• Refined BPS state counting from Nekrasov's formula and Macdonald functions
• ABCD of instantons
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• Refined Topological Vertex and Instanton Counting
• Quantum Algebraic Approach to Refined Topological Vertex
• Five-dimensional AGT Relation and the Deformed beta-ensemble
• BPS Bound States Of D0-D6 And D0-D8 Systems In A B-Field
• Quantum toroidal ${\mathfrak{gl}}_1$ algebra : plane partitions
• Explicit examples of DIM constraints for network matrix models
• BPS/CFT correspondence II: Instantons at crossroads, Moduli and Compactness Theorem
• Quantum continuous ${\mathfrak{gl}}_{\infty }$: Semi-infinite construction of representations
• BPS/CFT Correspondence III: Gauge Origami partition function and qq-characters
• The 3-fold vertex via stable pairs
• A note on instanton counting for N=2 gauge theories with classical gauge groups
• Quiver W-algebras
• BPS/CFT correspondence IV: sigma models and defects in gauge theory
• Webs of W-algebras
• (p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters
• Line defects and 5d instanton partition functions
• Quiver Yangian from Crystal Melting
• Spiked Instantons from Intersecting D-branes
• Opers, surface defects, and Yang-Yang functional
• Magnificent Four with Colors
• Quantum continuous $g{l}_{\infty }$: Tensor products of Fock modules and $W_n$ characters
• Quiver Yangian and Supersymmetric Quantum Mechanics
• Integral Representations of the Macdonald Symmetric Functions
• Shifted Quiver Yangians and Representations from BPS Crystals
• Coherent states in quantum ${\mathcal{W}}_{1+\infty }$ algebra and qq-character for 5d Super Yang-Mills
• Conifold Transitions in M-theory on Calabi-Yau Fourfolds with Background Fluxes
• $K$-theoretic DT/PT correspondence for toric Calabi-Yau 4-folds
• From SO/Sp instantons to W-algebra blocks
• Quiver elliptic W-algebras
• A slow review of the AGT correspondence
• Curve counting and DT/PT correspondence for Calabi-Yau 4-folds
• Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations
• Fractional quiver W-algebras
• Quiver Matrix Model and Topological Partition Function in Six Dimensions
• Crystal Melting and Wall Crossing Phenomena
• A Note on Quiver Quantum Toroidal Algebra
• Three Dimensional N=2 Gauge Theories and Degenerations of Calabi-Yau Four-Folds
• Higher rank K-theoretic Donaldson-Thomas theory of points
• Quantum toroidal algebras and solvable structures in gauge/string theory
• Instanton counting and O-vertex
• More on topological vertex formalism for 5-brane webs with O5-plane
• ADHM in 8d, coloured solid partitions and Donaldson-Thomas invariants on orbifolds
• $q$-Deformation of Corner Vertex Operator Algebras by Miura Transformation
• Canonical vertex formalism in DT theory of toric Calabi-Yau 4-folds
• Quadratic relations of the deformed $W$-superalgebra ${\mathcal{W}}_{q,t}(\mathfrak{sl}(2|1))$
• Elliptic non-Abelian Donaldson-Thomas invariants of ${\mathbb{C}}^3$
• Tetrahedron instantons
• Quadratic relations of the deformed $W$-superalgebra ${\mathcal{W}}_{q,t}(A(M,N))$
• The Origin of Calabi-Yau Crystals in BPS States Counting
• ABCD of qq-characters
• Gauge origami and quiver W-algebras
• Integrating over quiver variety and BPS/CFT correspondence
• Tetrahedron instantons in Donaldson-Thomas theory
• Noncommutative Instantons in Diverse Dimensions
• SU(N) transitions in M-theory on Calabi-Yau fourfolds and background fluxes
• Instantons on Young diagrams with matters

Cited by in corpus (4)

• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• An Overview of Crystals and Double Quiver Yangians
• Gauge origami and quiver W-algebras IV: Pandharipande--Thomas $qq$-characters
• The 4-fold Pandharipande--Thomas vertex and Jeffrey--Kirwan residue