Maeda, Yoshiaki and Sako, Akifumi. (2012) Noncommutative deformation of spinor zero mode and Atiyah-Drinfeld-Hitchin-Manin construction. Journal of Mathematical Physics, Vol.53 (No.2). 022303. ISSN 00222488

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Abstract

A method to construct noncommutative instantons as deformations from commutative instantons was provided by Maeda and Sako [J. Geom. Phys. 58, 1784 (2008)]10.1016/j.geomphys.2008.08.006. Using this noncommutative deformed instanton, we investigate the spinor zero modes of the Dirac operator in a noncommutative instanton background on noncommutative 4, and we modify the index of the Dirac operator on the noncommutative space slightly and show that the number of the zero mode of the Dirac operator is preserved under the noncommutative deformation. We prove the existence of the Green's function associated with instantons on noncommutative 4, as a smooth deformation of the commutative case. The feature of the zero modes of the Dirac operator and the Green's function derives noncommutative ADHM (Atiyah-Drinfeld-Hitchin-Manin) equations which coincide with the ones introduced by Nekrasov and Schwarz. We show a one-to-one correspondence between the instantons on noncommutative 4 and ADHM data. An example of a noncommutative instanton and a spinor zero mode are also given.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Journal of Mathematical Physics
Publisher:	American Institute of Physics
ISSN:	00222488
Date:	2 February 2012
Volume:	Vol.53
Number:	No.2
Page Range:	022303
Identification Number:	10.1063/1.3679398
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/44886

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