Nonlinear PDE aspects of the tt* equations of cecotti and vafa
Journal
Journal fur die Reine und Angewandte Mathematik
Journal Issue
689
Pages
1-32
Date Issued
2014
Author(s)
Guest, M.A.
Abstract
Using nonlinear pde techniques, we construct a new family of globally smooth tt* structures. This includes tt* structures associated to the (orbifold) quantum cohomology of a finite number of complex projective spaces and weighted projective spaces. The existence of such "magical solutions" of the tt* equations, namely smooth solutions characterised by asymptotic boundary conditions, was predicted by Cecotti and Vafa. In our situation, the tt* equations belong to a class of equations which we call the tt-Toda lattice. Solutions of the tt-Toda lattice are harmonic maps which have dual interpretations as Frobenius structures or variations of (semi-infinite) Hodge structures. © De Gruyter 2014.
SDGs
Type
journal article