Extended complex Yang–Mills instanton sheaves

Abstract

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