Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-06-29
Phys.Lett. B488 (2000) 194-198
Physics
High Energy Physics
High Energy Physics - Theory
7 pages, one comment plus reference added, version to be published in Phys. Lett. B
Scientific paper
10.1016/S0370-2693(00)00872-8
This note addresses the question of the number of normalizable vacuum states in supersymmetric quantum mechanics with sixteen supercharges and arbitrary semi-simple compact gauge group, up to rank three. After evaluating certain contour integrals obtained by appropriately adapting BRST deformation techniques we propose novel rational values for the bulk indices. Our results demonstrate that an asymptotic method for obtaining the boundary contribution to the index, originally due to Green and Gutperle, fails for groups other than SU(N). We then obtain likely values for the number of ground states of these systems. In the case of orthogonal and symplectic groups our finding is consistent with recent conjectures of Kac and Smilga, but appears to contradict their result in the case of the exceptional group G_2.
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