Quantum Gravity 255.1: The Multi-Instanton 8k - 3 (Fundamental Set) Expression From U.K., Turkey, Italy, Netherlands

From Osher Doctorow

The Multi-Instanton 8k - 3 expression has been known for quite some
years and appears to go back to M. Atiyah, N. J. Hitchin, I. M.
Singer, "Deformations of instantons," Proc. Nat. Acadm. Sci. USA, 74A
(1977), 2662-2663. It has recently been generalized together with
other aspects of Multi-Instantons in "Noncommutative families of
instantons," Giovanni Landi, Chiara Pagani, Cesare Reina, Walter D.
van Suijlekom, respectively U. di Trieste Italy, U. Copenhagen,
International School for Advanced Studies Trieste Italy, U.
Netherlands, arXiv: 0710.0721 v2 [math.QA] 15 May 2008, 25 pages, and
"The 8k - 3 Instanton," by Khaled Abdel-Khalek of Feza Gursey
Institute Turkey in arXiv: hep-th/0105297 v1 29 May 2001, 10 pages,
and also Bayrom Texin's (U. Oxford) "Multi-instantons in R^4 and
minimal surfaces," arXiv: hep-th 10006135 v1 17 Jun 2000, 14 pages.

I'll let Readers look at the papers and just mention here, e.g., that
8k - 3 is:

1) 8k - 3 = 2^3 k - 3

and takes the value 5 for k = 1 (e.g., vacuum), and the value 13 for k
= 2, which are two numbers in the Fundamental PI Set {0, 1, 2, 3, 4,
5, 7, 10, 11, 13, 26}, and that the numbers 2 and 3 of 2^3k - 3 of (1)
are all in the Fundamental set.

Multi-instantons on a line in R^4 are finite action solutions of the
dual-dual Yang-Mills field.

We also have:

2) topological number = k - 1
3) topological charge of the theory for 4 dimensions is Q = k - 1, k
as in (2)
4) The true number of parameters is 8k - 3 for any k-instanton, of
which 8k are real and the dimension of the automorphism group is 3.
5) From the index theorem, the most general instanton has 8k - 3 real
parameters.
6) The main gauge group considered is SU(2).

Osher Doctorow
.

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