Witten’s D ₄ integrable hierarchies conjecture

Abstract

The authors prove that the total descendant potential functions of the theory of Fan-Jarvis-Ruan-Witten for D ₄ with symmetry group 〈J〉 and for D ₄ ^T with symmetry group G _max, respectively, are both tau-functions of the D ₄ Kac-Wakimoto/Drinfeld-Sokolov hierarchy. This completes the proof, begun in the article by Fan-Jarvis-Ruan (2013), of the Witten Integrable Hierarchies Conjecture for all simple (ADE) singularities.

Keywords

Quantum cohomology / Frobenius manifolds / Singularity theory / Integrable hierarchies

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