Extended complex Yang–Mills instanton sheaves

Abstract

In the search of 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 [4] or 0 on some points of CP 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 SU (2) complex YM instantons [3]. We then show that in the new "extended complex YM instantons" discovered in this paper, rank β can be either 2 on the whole CP 3 (bundle) with some given ADHM data or 1, 0 on some points of CP 3 with other ADHM data (sheaves). These extended SU (2) complex YM instantons have no real instanton counterparts. * Electronic address: