A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds

Abstract

Let $G$ be a finite subgroup of $\mathrm{SU}(4)$ whose elements have age not larger than one. In the first part of this paper, we define $K$-theoretic stable pair invariants on the crepant resolution of the affine quotient ${\mathbb{C}}^4/G$, and conjecture closed formulae for their generating series, expressed in terms of the root system of $G$. In the second part, we define degree zero Donaldson-Thomas invariants of Calabi-Yau 4-orbifolds, develop a vertex formalism that computes the invariants in the toric case and conjecture closed formulae for the quotient stacks $[{\mathbb{C}}^4/{\mathbb{Z}}_r]$, $[{\mathbb{C}}^4/{\mathbb{Z}}_2\times {\mathbb{Z}}_2]$. Combining these two parts, we formulate a crepant resolution correspondence which relates the above two theories.

41 pages. Published version

References in corpus (5)

• Enumerative geometry of Calabi-Yau 4-folds
• Canonical vertex formalism in DT theory of toric Calabi-Yau 4-folds
• Noncommutative Instantons in Diverse Dimensions
• Double Quiver Gauge Theory and BPS/CFT Correspondence
• On the M2-Brane Index on Noncommutative Crepant Resolutions

Cited by in corpus (1)

• Tetrahedron instantons in Donaldson-Thomas theory