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.

66+13 pages, v2: published version

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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