D-particles on orientifolds and rational invariants

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 N = 16 $mathcal{N}=16$ 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.