Quantum D_4 Drinfeld–Sokolov hierarchy and quantum singularity theory

Abstract : In this paper we compute explicitly the double ramification hierarchy and its quan-tization for the D_4 Dubrovin-Saito cohomological field theory obtained applying the Givental-Teleman reconstruction theorem to the D_4 Coxeter group Frobenius manifold, or equivalently the D_4 Fan-Jarvis-Ruan-Witten cohomological field theory (with respect to the non-maximal diagonal symmetry group J = Z/3Z). We then prove its equivalence to the corresponding Dubrovin-Zhang hierarchy, which was known to coincide with the D_4 Drinfeld-Sokolov hierarchy. Our techniques provide hence an explicit quantization of the D_4 Drinfeld-Sokolov hierarchy. Moreover, since the DR hierarchy is well defined for partial CohFTs too, our approach immediately computes the DR hierarchies associated to the invariant sectors of the D_4 CohFT with respect to folding of the Dynkin diagram, the B_3 and G_2 Drinfeld-Sokolov hierarchies.
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Contributor : Ann Du Crest de Villeneuve <>
Submitted on : Sunday, February 17, 2019 - 4:19:56 PM
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Ann Du Crest de Villeneuve, Paolo Rossi. Quantum D_4 Drinfeld–Sokolov hierarchy and quantum singularity theory. 2019. ⟨hal-02022209⟩

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