Extended Complex Yang-Mills Instanton Sheaves

TL;DR

This paper explores extended complex Yang-Mills instanton sheaves with topological charge two, revealing new configurations where the rank of the beta matrix varies, and demonstrating the non-existence of certain sheaf cases within previous constructions.

Contribution

It introduces extended complex YM instantons allowing variable beta matrix rank and shows the non-existence of rank zero sheaves in earlier models.

Findings

Rank zero sheaves do not exist in previous constructions.

Extended instantons can have beta rank 2 or 1, 0 on some points of CP^3.

These instantons have no real instanton counterparts.

Abstract

In the search of YM instanton sheaves with topological charge two, the rank of beta matrix in the monad construction can be dropped from the bundle case with rank(beta)= 2 to either rank(beta) = 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(beta)= 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(beta) 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.