Tetrahedron instantons in Donaldson-Thomas theory

Abstract

Inspired by the work of Pomoni-Yan-Zhang in String Theory, we introduce the moduli space of tetrahedron instantons as a Quot scheme and describe it as a moduli space of quiver representations. We construct a virtual fundamental class and virtual structure sheaf à la Oh-Thomas, by which we define K-theoretic invariants. We show that the partition function of such invariants reproduces the one studied by Pomoni-Yan-Zhang, and explicitly determine it, as a product of shifted partition functions of rank one Donaldson-Thomas invariants of the three-dimensional affine space. Our geometric construction answers a series of questions of Pomoni-Yan-Zhang on the geometry of the moduli space of tetrahedron instantons and the behaviour of its partition function, and provides a new application of the recent work of Oh-Thomas.

33 pages, typos fixed, final version to appear in Advances in Mathematics

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Cited by in corpus (6)

• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• Hyperquot schemes on curves: virtual class and motivic invariants
• 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
• Invariants of nested Hilbert and Quot schemes on surfaces