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arXiv · 1610.00182

On the Stokes matrices of the $tt^*$-Toda equation

Stefan Horocholyn
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Abstract

We derive a formula for the signature of the symmetrized Stokes matrix $\cal{S}+\cal{S}^\mathrm{T}$ for the $tt^*$-Toda equation. As a corollary, we verify a conjecture of Cecotti and Vafa regarding when $\cal{S}+\cal{S}^\mathrm{T}$ is positive definite, reminiscent of a formula of Beukers and Heckmann for the generalized hypergeometric equation. The condition that $\cal{S}+\cal{S}^\mathrm{T}$ is positive definite is prominent in the work of Cecotti and Vafa on the $tt^*$ equation; we show that the Stokes matrices $\cal{S}$ satisfying this condition are parameterized by the points of an open convex polytope.

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Stefan Horocholyn. 2017-01-27. On the Stokes matrices of the $tt^*$-Toda equation. https://arxiv.org/abs/1610.00182

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