Witten's D_4 Integrable Hierarchies Conjecture
Huijun Fan, Amanda Francis, Tyler J. Jarvis, Evan Merrell, Yongbin, Ruan
TL;DR
This paper proves that the total descendant potential functions for certain D_4 singularity theories are tau-functions of the D_4 integrable hierarchy, completing the proof of Witten's conjecture for all ADE singularities.
Contribution
It establishes the connection between Fan-Jarvis-Ruan-Witten theories for D_4 and the D_4 integrable hierarchy, confirming Witten's conjecture for all simple singularities.
Findings
Total descendant potential functions are tau-functions of D_4 hierarchy.
Completes proof of Witten's Integrable Hierarchies Conjecture for ADE singularities.
Links FJRW theories with integrable hierarchies.
Abstract
We prove that the total descendant potential functions of the theory of Fan-Jarvis-Ruan-Witten for D_4 with symmetry group <J> and 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 [FJR], of the Witten Integrable Hierarchies Conjecture for all simple (ADE) singularities.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Nonlinear Waves and Solitons