Categorical wall-crossing formula for Donaldson-Thomas theory on the resolved conifold

TL;DR

This paper establishes a categorical wall-crossing formula for Donaldson-Thomas invariants on the resolved conifold, providing a categorification of existing numerical formulas and deriving new semiorthogonal decompositions.

Contribution

It introduces a categorical wall-crossing formula for DT invariants on the resolved conifold, extending previous numerical results to a categorical framework.

Findings

Categorifies Nagao-Nakajima wall-crossing formula

Derives semiorthogonal decompositions of categorical PT invariants

Provides a new perspective on DT and PT invariants via categorical methods

Abstract

We prove wall-crossing formula for categorical Donaldson-Thomas invariants on the resolved conifold, which categorifies Nagao-Nakajima wall-crossing formula for numerical DT invariants on it. The categorified Hall products are used to describe the wall-crossing formula as semiorthogonal decompositions. A successive application of categorical wall-crossing formula yields semiorthogonal decompositions of categorical Pandharipande-Thomas stable pair invariants on the resolved conifold, which categorify the product expansion formula of the generating series of numerical PT invariants on it.