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Nahm transforms

  • Claudio BartocciEmail author
  • Ugo Bruzzo
  • Daniel Hernández Ruipérez
Chapter
Part of the Progress in Mathematics book series (PM, volume 276)

Abstract

The original Nahm transform, i.e., a mechanism that starting from an instanton on a 4-dimensional at torus produces an instanton on the dual torus, was introduced by Nahm in 1983 [230]. This construction was formalized by Schenk [263] and Braam and van Baal [57] in later years. Their descriptions show that the Nahm transform is essentially an index-theoretic construction: given a vector bundle E on at torus X, equipped with an anti-self-dual connection ∇, one considers the dual torus \(\hat{X}\) as a space parameterizing a family of Dirac operators twisted by ∇. Taking the index of this family yields, under suitable conditions, the instanton \(\hat{\nabla}\) on \(\hat{X}\) .

Keywords

Modulus Space Vector Bundle Line Bundle Dirac Operator Ahler Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  • Claudio Bartocci
    • 1
    Email author
  • Ugo Bruzzo
    • 2
  • Daniel Hernández Ruipérez
    • 3
  1. 1.Dipartimento di MatematicaUniversità di GenovaGenovaItaly
  2. 2.Scuola Internazionale Superiore di Studi Avanzati and Istituto Nazionale di Fisica NucleareTriesteItaly
  3. 3.Departamento de Matemáticas and Instituto Universitario de Fisica Fundamental y MatemáticasUniversidad de SalamancaSalamancaSpain

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