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Once more on the Witten index of 3d supersymmetric YM-CS theory
Smilga A.V.
Journal of High Energy Physics 1205 (2012) (2012) 103 - http://hal.in2p3.fr/in2p3-00702438
Physique/Physique des Hautes Energies - Théorie
Physique/Physique mathématique
Mathématiques/Physique mathématique
Once more on the Witten index of 3d supersymmetric YM-CS theory
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
The problem of counting the vacuum states in the supersymmetric 3d Yang-Mills-Chern-Simons theory is reconsidered. We resolve the controversy between its original calculation by Witten at large volumes and the calculation based on the evaluation of the effective Lagrangian in the small volume limit. We show that the latter calculation suffers from uncertainties associated with the singularities in the moduli space of classical vacua where the Born-Oppenheimer approximation breaks down. We also show that these singularities can be accurately treated in the Hamiltonian Born-Oppenheimer method, where one has to match carefully the effective wave functions on the Abelian valley and the wave functions of reduced non-Abelian QM theory near the singularities. This gives the same result as original Witten's calculation.

Articles dans des revues avec comité de lecture
2012
Journal of High Energy Physics
Publisher Institute of Physics (IOP)
ISSN 1126-6708 (eISSN : 1029-8479)
1205 (2012)
103

SUBATECH-TheorieHe
27 pages
Lien vers le texte intégral : 
http://fr.arXiv.org/abs/1202.6566