2020/11/15 by Yoshiki Kaneko, Kaneko, Yoshiki
Mathematics · #53D45 (Primary) 81T40 (Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2011.07436
openalex publication_date 2020/11/15 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28
We relate the quantum cohomology of minuscule flag manifolds to the tt*-Toda equations, a special case of the topological-antitopological fusion equations which were introduced by Cecotti and Vafa in their study of supersymmetric quantum field theories. To do this, we combine the Lie-theoretic treatment of the tt*-Toda equations of Guest-Ho with the Lie-theoretic description of the quantum cohomology of minuscule flag manifolds from Chaput-Manivel-Perrin and Golyshev-Manivel.