The threshold bound state conjecture for SU(N) supersymmetric matrix quantum mechanics

Theorem 1.1: for every integer $N\ge2$, the relative undeformed $\mathrm{SU}(N)$ BFSS Hamiltonian (closure of $\frac1{16}\sum_\alpha\|Q_\alpha\Psi\|^2$ on gauge-invariant states in $L^2(\mathbb R^{9(N^2-1)})$ tensor a Clifford module) has a one-dimensional kernel, consisting of $\mathrm{Spin}(9)$-invariant even states. This gives both existence and uniqueness of the threshold bound state at each finite $N$. Constants depend on $N$; nothing is claimed about large-$N$ limits or the matrix-theory conjecture itself.

Theorem 1.1: for every integer $N\ge2$, the relative undeformed $\mathrm{SU}(N)$ BFSS Hamiltonian (closure of $\frac1{16}\sum_\alpha\|Q_\alpha\Psi\|^2$ on gauge-invariant states in $L^2(\mathbb R^{9(N^2-1)})$ tensor a Clifford module) has a one-dimensional kernel, consisting of $\mathrm{Spin}(9)$-invariant even states. This gives both existence and uniqueness of the threshold bound state at each finite $N$. Constants depend on $N$; nothing is claimed about large-$N$ limits or the matrix-theory conjecture itself.