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

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## 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 |
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Divisions: | School of Theoretical Physics > Preprints |

Date Deposited: | 13 Jul 2018 14:12 |

Last Modified: | 15 Dec 2022 20:33 |

URI: | https://dair.dias.ie/id/eprint/583 |

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