ADHM Construction of Instantons on the Torus

Ford, C. and Pawlowski, J. M. and Tok, T. and Wipf, A. (2000) ADHM Construction of Instantons on the Torus. (Preprint)

Share Twitter Facebook Email

[img] Text
0005221.pdf

Download (316kB)

Abstract

We apply the ADHM instanton construction to SU(2) gauge theory on T^n x R^(4-n)for n=1,2,3,4. To do this we regard instantons on T^n x R^(4-n) as periodic (modulo gauge transformations) instantons on R^4. Since the R^4 topological charge of such instantons is infinite the ADHM algebra takes place on an infinite dimensional linear space. The ADHM matrix M is related to a Weyl operator (with a self-dual background) on the dual torus tilde T^n. We construct the Weyl operator corresponding to the one-instantons on T^n x R^(4-n). In order to derive the self-dual potential on T^n x R^(4-n) it is necessary to solve a specific Weyl equation. This is a variant of the Nahm transformation. In the case n=2 (i.e. T^2 x R^2) we essentially have an Aharonov Bohm problem on tilde T^2. In the one-instanton sector we find that the scale parameter, lambda, is bounded above, (lambda)^2 tv<4 pi, tv being the volume of the dual torus tilde T^2.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 13 Jul 2018 14:12
Last Modified: 27 Jul 2018 10:58
URI: http://dair.dias.ie/id/eprint/583

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year