A \(tt^*\)-bundle associated with a harmonic map from a Riemann surface into a sphere. (English) Zbl 1250.53062
A \(tt^*\)-bundle is a real vector bundle equippled with a family of flat connections, parametrized by a circle. The notion of \(tt^*\)-bundle was introduced by Schäfer as a simple solution to a generalized version of the equation of topological-antitopological fusion which is a special geometric structure of a Frobenius manifold.
In this paper, the authors construct a \(tt^*\)-bundle by using a harmonic map from a Riemann surface into an \(n\)-dimensional sphere. This \(tt^*\)-bundle is a high-dimensional analogue of a quaternionic line bundle with a Willmore connection.
In this paper, the authors construct a \(tt^*\)-bundle by using a harmonic map from a Riemann surface into an \(n\)-dimensional sphere. This \(tt^*\)-bundle is a high-dimensional analogue of a quaternionic line bundle with a Willmore connection.
Reviewer: Gabjin Yun (Yongin)
MSC:
| 53C43 | Differential geometric aspects of harmonic maps |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
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