ゲージ理論を用いた位相不変量の非可換変形

概要

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Solitons in gauge theories in noncommutative spaces had been constructed by using several methods. However we did not have noncommutative soliton solutions by using deformation quantization from solitons in commutative soliton solutions, and we did not have researches for such solutions. In this article, we report them for the case of instantons that are solitons in a 4-dimensional gauge theory. Deformation quantization of instanton solutions for U(N) (N > 1) gauge theory in R^4 is constructed and it is shown that their instanton numbers are preserved under the deformation quantization. We also derive the one-to-one correspondence between the instantons and ADHM data. This article is written as a report for summarizing works supported by the KAKENHI No.20740049 (Grant-in-Aid for Young Scientists (B)).
2011-12-16