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Vacuum structure in supersymmetric Yang-Mills theories with any gauge group
Kac V.G., Smilga A.V.
Dans The Many Faces of the Superworld: Yuri Golfand Memorial Volume, M. Shifman (Ed.) (2000) 185-234 - http://hal.in2p3.fr/in2p3-00195525
Mathématiques/Physique mathématique
Physique/Physique mathématique
Mathématiques/Théorie des groupes
Physique/Physique des Hautes Energies - Théorie
Vacuum structure in supersymmetric Yang-Mills theories with any gauge group
V. G. Kac, A.V. Smilga1
1 :  SUBATECH - Laboratoire SUBATECH Nantes
http://www-subatech.in2p3.fr/
CNRS : UMR6457 – IN2P3 – Université de Nantes – École Nationale Supérieure des Mines - Nantes
4, rue Alfred Kastler - 44070 Nantes Cedex 03
France
We consider the pure supersymmetric Yang--Mills theories placed on a small 3-dimensional spatial torus with higher orthogonal and exceptional gauge groups. The problem of constructing the quantum vacuum states is reduced to a pure mathematical problem of classifying the flat connections on 3-torus. The latter problem is equivalent to the problem of classification of commuting triples of elements in a connected simply connected compact Lie group which is solved in this paper. In particular, we show that for higher orthogonal SO(N), N > 6, and for all exceptional groups the moduli space of flat connections involves several distinct connected components. The total number of vacuumstates is given in all cases by the dual Coxeter number of the group which agrees with the result obtained earlier with the instanton technique.

Chapitres d'ouvrages scientifiques
2000
The Many Faces of the Superworld: Yuri Golfand Memorial Volume
M. Shifman
185-234
World Scientific

41 pages, 9 figures, 9 tables. Final version to be published in the Yuri Golfand memorial volume. We added the Appendix D with classification of all non-trivial commuting n-tuples for arbitrary n
Lien vers le texte intégral : 
http://fr.arXiv.org/abs/hep-th/9902029