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Remarks on the Atiyah‐Hitchin Metric
Author(s) -
Bakas Ioannis
Publication year - 2000
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/(sici)1521-3978(20001)48:1/3<9::aid-prop9>3.0.co;2-7
Subject(s) - twistor theory , moduli space , uniformization (probability theory) , supersymmetry , quantum field theory , gauge theory , connection (principal bundle) , context (archaeology) , mathematical physics , mathematics , instanton , moduli of algebraic curves , pure mathematics , physics , geometry , paleontology , statistics , balance equation , markov model , markov chain , biology
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.