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 $\mathcal{N}=16$ $O(m)$ 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.

38 pages

References in corpus (5)

• Counting Gauge Invariants: the Plethystic Program
• Witten Index and Wall Crossing
• Wall-Crossing from Boltzmann Black Hole Halos
• Twisted Partition Functions and $H$-Saddles
• M5-branes, orientifolds, and S-duality

Cited by in corpus (3)

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• Holonomy Saddles and Supersymmetry
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