Nonlinear PDE aspects of the tt* equations of cecotti and vafa

Martin A. Guest, Chang Shou Lin

Research output: Contribution to journalArticle

7 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1-32
Number of pages32
JournalJournal fur die Reine und Angewandte Mathematik
Issue number689
DOIs
Publication statusPublished - 2014 Apr

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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