Remarks on the Atiyah-Hitchin Metric

✍ Scribed by Ioannis Bakas

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 70 KB
• Volume: 48
• Category: Article
• ISSN: 0015-8208
• DOI: 10.1002/(sici)1521-3978(20001)48:1/3<9::aid-prop9>3.0.co;2-7

✦ Synopsis

We outline the construction of the Atiyah-Hitchin metric on the moduli space of SU (2) BPS monopoles with charge 2, first as an algebraic curve in C 3 following Donaldson and then as a solution of the Toda field equations in the continual large N limit. We adopt twistor methods to solve the underlying uniformization problem, which by the generalized Legendre transformation yield the Kähler coordinates and the Kähler potential of the metric. We also comment on the connection between twistors and the Seiberg-Witten construction of quantum moduli spaces, as they arise in three dimensional supersymmetric gauge theories, and briefly address the uniformization of algebraic curves in C 3 in the context of large N Toda theory.