A Lie-theoretic Description of the Solution Space of the tt*-Toda Equations

Martin A. Guest*, Nan Kuo Ho

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We give a Lie-theoretic explanation for the convex polytope which parametrizes the globally smooth solutions of the topological-antitopological fusion equations of Toda type (tt -Toda equations) which were introduced by Cecotti and Vafa. It is known from Guest and Lin (J. Reine Angew. Math. 689, 1–32 2014) Guest et al. (It. Math. Res. Notices 2015, 11745–11784 2015) and Mochizuki (2013, 2014) that these solutions can be parametrized by monodromy data of a certain flat SLn+ 1ℝ-connection. Using Boalch’s Lie-theoretic description of Stokes data, and Steinberg’s description of regular conjugacy classes of a linear algebraic group, we express this monodromy data as a convex subset of a Weyl alcove of SUn+ 1.

Original languageEnglish
Article number24
JournalMathematical Physics Analysis and Geometry
Issue number4
Publication statusPublished - 2017 Dec 1


  • Monodromy
  • tt*-Toda equations

ASJC Scopus subject areas

  • Mathematical Physics
  • Geometry and Topology


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