Abstract
We revisit the D0 bound state problems, of the M/IIA duality, with the Orientifolds. The cases of O4 and O8 have been studied recently, from the perspective of five-dimensional theories, while the case of O0 has been much neglected. The computation we perform for D0-O0 states boils down to the Witten indices for \( \mathcal{N}=16 \) O(m) and Sp(n) quantum mechanics, where we adapt and extend previous analysis by the authors. The twisted partition function Ω, obtained via localization, proves to be rational, and we establish a precise relation between Ω and the integral Witten index ℐ, by identifying continuum contributions sector by sector. The resulting Witten index shows surprisingly large numbers of threshold bound states but in a manner consistent with M-theory. We close with an exploration on how the ubiquitous rational invariants of the wall-crossing physics would generalize to theories with Orientifolds.
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Lee, SJ., Yi, P. D-particles on orientifolds and rational invariants. J. High Energ. Phys. 2017, 46 (2017). https://doi.org/10.1007/JHEP07(2017)046
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DOI: https://doi.org/10.1007/JHEP07(2017)046