Nahm transforms

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


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 \(\hat{X}\) .


Modulus Space Vector Bundle Line Bundle Dirac Operator Ahler Manifold 
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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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