On stability of baryonic black membranes

Abstract: Near-extremal black membranes with topological (baryonic) $U(1)B$ charge of M-theory compactified on the coset space $M^{1,1,0}$ are stable. $M^{1,1,0}$ coset is a ${\mathbb Z}_2$-invariant truncation of a larger $Q^{1,1,1}$ coset, with diagonal $U(1)_B\equiv U(1){B,+}\subset U(1)B^2$ symmetry of the latter. We show that the baryonic black membranes of M-theory $M^{1,1,0}$ compactifications are unstable to ${\mathbb Z}_2$-odd gravitational bulk gauge and scalar fluctuations, but only if this bulk scalar is identified with the holographically dual $2+1$ dimensional superconformal gauge theory operator of conformal dimension $Δ=1$. The instability is associated with the unstable charge transport of the off-diagonal $U(1){B,-}\subset U(1)_B^2$ symmetry.