Canonical vertex formalism in DT theory of toric Calabi-Yau 4-folds

TL;DR

This paper introduces a canonical vertex formalism for computing Donaldson-Thomas invariants of toric Calabi-Yau 4-folds, utilizing combinatorics of partitions to establish square roots and sign rules.

Contribution

It develops a canonical vertex formalism with sign rules for DT invariants, advancing the computational framework for toric Calabi-Yau 4-folds.

Findings

Proposed square roots and sign rules for vertex and edge contributions.

Proved the canonicity of the formalism using combinatorics of partitions.

Enhanced the computational methods for DT invariants in toric Calabi-Yau 4-folds.

Abstract

Motivated by previous computations of Y. Cao, M. Kool and the author, we propose square roots and sign rules for the vertex and edge terms that compute Donaldson-Thomas invariants of a toric Calabi-Yau 4-fold, and prove that they are canonical, exploiting the combinatorics of plane and solid partitions.