Sheaf lines of Yang-Mills instanton sheaves

Abstract

We calculate a sheaf line in CP3 which is the real line supporting sheaf points on CP3 of SL(2, C) Yang-Mills (YM) instanton (or SU(2) complex YM instanton) sheaves for some given ADHM data we obtained previously. We found that this sheaf line is indeed a special jumping line over S-4 spacetime. In addition, we calculate the singularity structure of the connection A and the field strength F at the corresponding singular point on S-4 of this sheaf line. We found that the order of singularity at the singular point on S-4 associated with the sheaf line in CP3 is higher than those of other singular points associated with normal jumping lines. We conjecture that this is a general feature for sheaf lines among jumping lines.