Drinfeld-Manin instanton and its noncommutative generalization

TIAN Yu

doi:10.1088/1674-1137/34/10/002

Chinese Physics C> 2010, Vol. 34> Issue(10) : 1556-1564 DOI: 10.1088/1674-1137/34/10/002

Drinfeld-Manin instanton and its noncommutative generalization

TIAN Yu ^,

College of Physical Sciences, Graduate University of the Chinese Academy of Sciences, Beijing 100049, China

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Abstract：
The Drinfeld-Manin construction of U(N) instanton is reformulated in the ADHM formulism, which gives explicit general solutions of the ADHM constraints for U(N) (N≥2k－1) k-instantons. For the N<2k-1 case, implicit results are given systematically as further constraints. We find that this formulism can easily be generalized to the noncommutative case, where the explicit solutions are also obtained.

References

[1]

Coleman S.Uses of Instantons.Cambridge:Cambridge University Press,1985[2] Rajaraman R.Solitons and Instantons.Amsterdam:North-Holland Publishing Company,1982[3] Schfer T,Shuryak E V.Rev.Mod.Phys.,1998,70:323[4] Shifman M A,Vainshtein A I.Instantons Versus Supersymmetry:Fifteen Years Later.In:Shifman M A.ITSP Lectures on Particle Physics and Field Theory.Singapore:World Scientific,1999.485-648[5] Freed D S,Uhlenbeck K K.Instantons and Four-Manifolds.New York:Springer-Verlag,1984[6] Donaldson S K,Kronheimer P B.The Geometry of FourManifolds.Oxford:Clarendon Press,1990[7] Belavin A A,Polyakov A M,Shvarts A S,Tyupkin Y S.Phys.Lett.B,1975,59:85[8] Atiyah M F,Hitchin N J,Drinfeld V G,Manin Y I.Phys.Lett.A,1978,65:185[9] Christ N H,Weinberg E J,Stanton N K.Phys.Rev.D,1978,18:2013-2025[10] Korepin V E,Shatashvili S L.Sov.Phys.Dokl.,1983,28:1018-1019[11] TIAN Yu.Phys.Lett.B,2003,566:183-185[12] TIAN Yu,ZHU Chuan-Jie,SONG Xing-Chang.Mod.Phys.Lett.A,2003,18:1691-1703[13] Dorey N,Hollowood T J,Khoze V V,Mattis M P,Vandoren S.Nucl.Phys.B,1999,552:88-168; Dorey N,Hollowood T J,Khoze V V,Mattis M P.Phys.Rept.,2002,371:231-459[14] Konechny A,Schwarz A.Phys.Rept.,2002,360:353-465[15] Douglas M R,Nekrasov N A.Rev.Mod.Phys.,2002,73:977[16] Szabo R J.Phys.Rept.,2003,378:207-299[17] Seiberg N,Witten E.J.High Energy Phys.,1999,9909:032[18] Nakajima H.Lectures on Hilbert Schemes of Points on Surfaces.Providence:AMS Bookstore,1999[19] Nekrasov N,Schwarz A.Commun.Math.Phys.,1998,198:689[20] TIAN Yu,ZHU Chuan-Jie.Phys.Rev.D,2003,67:045016[21] Witten E.Nucl.Phys.B,1996,460:541[22] Douglas M R.Branes within Branes.[hep-th/9512077][23] Douglas M R,Moore G.D-branes,Quivers and ALE Instantous.[hep-th/9603167][24] Lee K,Tong D,Yi S.Phys.Rev.D,2001,63:065017[25] Drinfeld V G,Manin Y I.Commun.Math.Phys.,1978,63:177[26] Nekrasov N.Trieste Lectures on Solitons in Noneommutative Gauge Theories.[hep-th/0011095][27] Connes A.Noncommutative Geometry.San Diego:Academic Press,1994[28] Madore J.An Introduction to Noncommutative Geometry and its Physical Applications.Cambridge:Cambridge University Press,1999[29] Minwalla S,Raamsdonk M V,Seiberg N.J.High Energy Phys.,2000,0002:020[30] Furuuchi K.Prog.Theor.Phys.,2000,103:1043

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[20]	Ni Guang-jiong . THE LEVINSON THEOREM AND ITS GENERALIZATION IN RELATIVISTIC QUANTUM MECHANICS. Chinese Physics C, 1979, 3(4): 432-449.

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TIAN Yu. Drinfeld-Manin instanton and its noncommutative generalization[J]. Chinese Physics C, 2010, 34(10): 1556-1564. doi: 10.1088/1674-1137/34/10/002

TIAN Yu. Drinfeld-Manin instanton and its noncommutative generalization[J]. Chinese Physics C, 2010, 34(10): 1556-1564. doi: 10.1088/1674-1137/34/10/002 shu

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Received: 2009-11-25
Revised: 2010-01-08

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沈阳化工大学材料科学与工程学院沈阳 110142

Drinfeld-Manin instanton and its noncommutative generalization

Corresponding author: TIAN Yu,

College of Physical Sciences, Graduate University of the Chinese Academy of Sciences, Beijing 100049, China

Received Date: 2009-11-25

Accepted Date: 2010-01-08

Available Online: 2010-10-05

Abstract:

The Drinfeld-Manin construction of U(N) instanton is reformulated in the ADHM formulism, which gives explicit general solutions of the ADHM constraints for U(N) (N≥2k－1) k-instantons. For the N<2k-1 case, implicit results are given systematically as further constraints. We find that this formulism can easily be generalized to the noncommutative case, where the explicit solutions are also obtained.

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Drinfeld-Manin instanton and its noncommutative generalization

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