### Abstract

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 SL_{n+ 1}ℝ-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 SU_{n+ 1}.

Original language | English |
---|---|

Article number | 24 |

Journal | Mathematical Physics Analysis and Geometry |

Volume | 20 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2017 Dec 1 |

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### Keywords

- Monodromy
- tt*-Toda equations

### ASJC Scopus subject areas

- Mathematical Physics
- Geometry and Topology

### Cite this

**A Lie-theoretic Description of the Solution Space of the tt*-Toda Equations.** / Guest, Martin; Ho, Nan Kuo.

Research output: Contribution to journal › Article

*Mathematical Physics Analysis and Geometry*, vol. 20, no. 4, 24. https://doi.org/10.1007/s11040-017-9255-z

}

TY - JOUR

T1 - A Lie-theoretic Description of the Solution Space of the tt*-Toda Equations

AU - Guest, Martin

AU - Ho, Nan Kuo

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

KW - Monodromy

KW - tt-Toda equations

UR - http://www.scopus.com/inward/record.url?scp=85032909948&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85032909948&partnerID=8YFLogxK

U2 - 10.1007/s11040-017-9255-z

DO - 10.1007/s11040-017-9255-z

M3 - Article

VL - 20

JO - Mathematical Physics Analysis and Geometry

JF - Mathematical Physics Analysis and Geometry

SN - 1385-0172

IS - 4

M1 - 24

ER -