Sheaf lines of Yang-Mills Instanton Sheaves
Abstract
We calculate a sheaf line in CP^3 which is the real line supporting sheaf points on CP^3 of SL(2,C) Yang-Mills instanton (or SU(2) complex Yang-Mills 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 CP^3 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.
Keywords
Cite
@article{arxiv.1708.02853,
title = {Sheaf lines of Yang-Mills Instanton Sheaves},
author = {Sheng-Hong Lai and Jen-Chi Lee and I-Hsun Tsai},
journal= {arXiv preprint arXiv:1708.02853},
year = {2020}
}
Comments
28 pages, no figuree. v2: 29 pages, typos corrected and equations added v3: 29 pages, typos corrected and equations added v4: "SU(2) complex YM instanton" added. v5: 34 pages, Secs IV.C.1-IV.C.3 added. v6: a subsection "Discussion" added in the end; Refs [6],[7],[26],[27],[29]-[35] and [38]-[42] added