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

Martin A. Guest; Nan Kuo Ho

doi:10.1007/s11040-017-9255-z

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

Martin A. Guest^*, Nan Kuo Ho

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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	https://doi.org/10.1007/s11040-017-9255-z
Publication status	Published - 2017 Dec 1

Keywords

Monodromy
tt*-Toda equations

ASJC Scopus subject areas

Mathematical Physics
Geometry and Topology

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10.1007/s11040-017-9255-z

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title = "A Lie-theoretic Description of the Solution Space of the tt*-Toda Equations",

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 SLn+ 1ℝ-connection. Using Boalch{\textquoteright}s Lie-theoretic description of Stokes data, and Steinberg{\textquoteright}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.",

keywords = "Monodromy, tt*-Toda equations",

author = "Guest, {Martin A.} and Ho, {Nan Kuo}",

note = "Funding Information: Acknowledgements The authors thank Philip Boalch, Ralf Kurbel, and Eckhard Meinrenken for useful conversations. The first author was partially supported by JSPS grant (A) 25247005. He is grateful to the National Center for Theoretical Sciences for excellent working conditions and financial support. The second author was partially supported by MOST grant 104-2115-M-007-004. She is grateful to the Japan Society for the Promotion of Science for the award of a Short-Term Invitation Fellowship. Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media B.V.",

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doi = "10.1007/s11040-017-9255-z",

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AU - Guest, Martin A.

AU - Ho, Nan Kuo

N1 - Funding Information: Acknowledgements The authors thank Philip Boalch, Ralf Kurbel, and Eckhard Meinrenken for useful conversations. The first author was partially supported by JSPS grant (A) 25247005. He is grateful to the National Center for Theoretical Sciences for excellent working conditions and financial support. The second author was partially supported by MOST grant 104-2115-M-007-004. She is grateful to the Japan Society for the Promotion of Science for the award of a Short-Term Invitation Fellowship. Publisher Copyright: © 2017, Springer Science+Business Media B.V.

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.

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KW - tt-Toda equations

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

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