Nonlinear PDE aspects of the tt* equations of Cecotti and Vafa

Details Nonlinear PDE aspects of the tt* equations of Cecotti and Vafa Nonlinear PDE aspects of the tt* equations of Cecotti and Vafa

2010-10-10

arxiv.org/abs/1010.1889v1

Physics

Mathematical Physics

35 pages

Scientific paper

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 characterized 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.

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