arXiv Open Access 2009

The tt* structure of the quantum cohomology of CP^1 from the viewpoint of differential geometry

Josef Dorfmeister Martin Guest Wayne Rossman

Lihat Sumber

Abstrak

The quantum cohomology of CP^1 provides a distinguished solution of the third Painleve equation. S. Cecotti and C. Vafa discovered this from a physical viewpoint. We derive it from a differential geometric viewpoint, using the theory of harmonic maps and in particular the generalized Weierstrass representation (DPW representation) for spacelike surfaces of constant mean curvature in Minkowski space. The nontrivial aspects are the characterization of the solution, and its global behaviour. From our point of view, the latter property says that the extended harmonic map remains entirely within a single Iwasawa orbit of the appropriate loop group.

Topik & Kata Kunci

math.DG

Penulis (3)

Josef Dorfmeister

Martin Guest

Wayne Rossman

Format Sitasi

APA MLA BibTeX

Dorfmeister, J., Guest, M., Rossman, W. (2009). The tt* structure of the quantum cohomology of CP^1 from the viewpoint of differential geometry. https://arxiv.org/abs/0905.3876

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Informasi Jurnal

Tahun Terbit: 2009
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓