Landscape of superconducting membranes

Abstract

The AdS/CFT correspondence may connect the landscape of string vacua and the ``atomic landscape'' of condensed matter physics. We study the stability of a landscape of IR fixed points of $\mathcal{N}=2$ large $N$ gauge theories in $2+1$ dimensions, dual to Sasaki-Einstein compactifications of M theory, toward a superconducting state. By exhibiting instabilities of charged black holes in these compactifications, we show that many of these theories have charged operators that condense when the theory is placed at a finite chemical potential. We compute a statistical distribution of critical superconducting temperatures for a subset of these theories. With a chemical potential of 1 mV, we find critical temperatures ranging between 0.24 and 165 K.