D-Particles on Orientifolds and Rational Invariants

Understand

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 $\Omega$, obtained via localization, proves to be rational, and we establish a precise relation between $\Omega$ and the integral Witten index $\mathcal I$, by identifying continuum contributions sector by sector.