Orientifold Points in M Theory

TL;DR

This work identifies the M-theory lift of the four orientifold points as an orbifold of the form $\mathbf{R}^9/\mathbf{Z}_2\times\mathbf{S}^1$ with a chiral fermion on the fixed circle, and shows that NS/R boundary conditions map to $SO(N)$ and $Sp(N)$ gauge sectors. By combining the mass-deformation index method with this M-theory picture, the authors reproduce the ground-state counts for $SO(N)$ and $Sp(N)$ as partitions into distinct odd and even parts, respectively, and relate these counts to a 1D chiral fermion on the fixed locus. Independent evidence from anomaly analyses and Casimir energy calculations in M theory confirms the proposed picture and its correspondence to the masses of orientifold points, while the Matrix theory formulation provides a DLCQ interpretation of M theory on $\mathbf{R}^9/\mathbf{Z}_2$. Overall, the paper unifies the Kac–Smilga index results with a concrete M-theory realization of orientifold points and clarifies their role in Matrix theory and DLCQ descriptions of M theory on orbifolds.

Abstract

We identify the lift to M theory of the four types of orientifold points, and show that they involve a chiral fermion on an orbifold fixed circle. From this lift, we compute the number of normalizable ground states for the SO(N) and $Sp(N)$ supersymmetric quantum mechanics with sixteen supercharges. The results agree with known results obtained by the mass deformation method. The mass of the orientifold is identified with the Casimir energy.