Bulk Witten Indices and the Number of Normalizable Ground States in 
Supersymmetric Quantum Mechanics of Orthogonal, Symplectic and Exceptional 
Groups

Staudacher, Matthias

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Bulk Witten Indices and the Number of Normalizable Ground States in Supersymmetric Quantum Mechanics of Orthogonal, Symplectic and Exceptional Groups

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Staudacher, Matthias
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Staudacher, M. (2000). Bulk Witten Indices and the Number of Normalizable Ground States in Supersymmetric Quantum Mechanics of Orthogonal, Symplectic and Exceptional Groups. Physics Letters B, 488, 194-198.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5776-C

Abstract

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 G2.