Near-extremal membranes in M-theory

We consider near-extremal membranes embedded in M-theory, consistently truncated to gauged $\mathcal{N} = 2$ supergravity in four dimensions on the coset space $M^{1,1,0}$. These are holographically dual to $2 + 1$ dimensional superconformal gauge theory with $U(1)_R \times U(1)_B$ global symmetry. Turning on the chemical potential to either the $R$-symmetry or the baryonic symmetry gives access to the quantum critical regime of the boundary gauge theory. We study perturbative stability of the extremal limit, and demonstrate that membranes with topological (baryonic) charge are free from all known instabilities. $R$-charged membranes are free from the superconducting instabilities, but have unstable charge transport and instabilities associated with the condensation of the axions.