# D-Particles on Orientifolds and Rational Invariants

## TL;DR

This paper investigates D0 bound states on orientifolds, especially O0, using localization techniques to compute rational Witten indices, revealing large bound state counts consistent with M-theory and exploring their wall-crossing invariants.

## Contribution

It extends analysis of D0-O0 bound states by computing the twisted partition function and relating it to the Witten index, revealing new insights into rational invariants in orientifold theories.

## Key findings

- Witten index indicates large threshold bound states
- Rational twisted partition function relates to integral Witten index
- Results align with M-theory expectations

## 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 $\Omega$, 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. 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.