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Extended complex Yang–Mills instanton sheaves

Department of Electrophysics, National Chiao-Tung University, 1001 University Road, Hsinchu 300, Taiwan, Hsinchu/Taiwan, Republic of China,

E-mail Address: xgcj944137@gmail.com

Corresponding author.

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Jen-Chi Lee

Department of Electrophysics, National Chiao-Tung University, 1001 University Road, Hsinchu 300, Taiwan, Hsinchu/Taiwan, Republic of China,

E-mail Address: jcclee@cc.nctu.edu.tw

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, and

I-Hsun Tsai

Department of Mathematics, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan, Taipei/Taiwan, Republic of China

E-mail Address: ihtsai@math.ntu.edu.tw

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https://doi.org/10.1142/S0219887820500619Cited by:0 (Source: Crossref)

Abstract

In the search of Yang–Mills (YM) instanton sheaves with topological charge two, the rank of $β$ matrix in the monad construction can be dropped from the bundle case with rank $β = 2$ to either rank $β = 1$ [S. H. Lai, J. C. Lee and I. H. Tsai, Yang–Mills instanton sheaves, Ann. Phys.377 (2017) 446] or 0 on some points of ${C P}^{3}$ of the sheaf cases. In this paper, we first show that the sheaf case with rank $β = 0$ does not exist for the previous construction of $S U (2)$ complex YM instantons [S. H. Lai, J. C. Lee and I. H. Tsai, Biquaternions and ADHM construction of concompact $S L (2, C)$ Yang–Mills instantons, Ann. Phys.361 (2015) 14]. We then show that in the new “extended complex YM instantons” discovered in this paper, rank $β$ can be either 2 on the whole ${C P}^{3}$ (bundle) with some given ADHM data or 1, 0 on some points of ${C P}^{3}$ with other ADHM data (sheaves). These extended $S U (2)$ complex YM instantons have no real instanton counterparts. Finally, the potential applications to real physics systems are noted in the end of the paper.

Keywords:

AMSC: 14D21, 81T13, 32L10, 14H70

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