D-particles on orientifolds and rational invariants
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We revisit the DO bound state problems, of the M/IIA duality, with the Orientifolds. The cases of 04 and 08 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 N = 16 O(m) and Sp(n) quantum mechanics, where we adapt and extend previous analysis by the authors. The twisted partition function Omega, obtained via localization, proves to be rational, and we establish a precise relation between Omega 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.