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

Abstract

Let G be a finite subgroup of SUp4q such that its elements have age at most one. In the first part of this paper, we define K-theoretic stable pair invariants on a crepant resolution of the affine quotient C4{G, and conjecture a closed formula for their generating series in terms of the root system of G. In the second part, we define degree zero Donaldson-Thomas invariants of CalabiYau 4-orbifolds, develop a vertex formalism that computes the invariants in the toric case, and conjecture closed formulae for their generating series for the quotient stacks rC4{Zrs, rC4{Z2 ˆ Z2s. Combining these two parts, we formulate a crepant resolution correspondence which relates the above two theories.