A DONALDSON-THOMAS CREPANT RESOLUTION CONJECTURE ON CALABI-YAU 4-FOLDS

Let G be a finite subgroup of SU(4) 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 [C4/Zr], [C4/Z2 x Z2]. Combining these two parts, we formulate a crepant resolution correspondence which relates the above two theories.