Communications in Mathematical Physics

, Volume 249, Issue 3, pp 431–448 | Cite as

Space-Time Foam from Non-Commutative Instantons

  • Harry W  BradenEmail author
  • Nikita A. Nekrasov


We show that a U(1) instanton on non-commutative Open image in new window corresponds to a non-singular U(1) gauge field on a commutative Kähler manifold X which is a blowup of Open image in new window at a finite number of points. This gauge field on X obeys Maxwell’s equations in addition to the susy constraint F0,2=0. For instanton charge k the manifold X can be viewed as a space-time foam with b2k. A direct connection with integrable systems of Calogero-Moser type is established. We also make some comments on the non-abelian case.


Manifold Foam Finite Number Integrable System Direct Connection 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Dept. of Mathematics and StatisticsUniversity of EdinburghEdinburghScotland
  2. 2.Joseph Henry LaboratoriesPrinceton UniversityPrincetonUSA
  3. 3.Institute for Theoretical and Experimental PhysicsMoscowRussia
  4. 4.IHESBures-sur-YvetteFrance

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