Landscape of superconducting membranes

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 N=2 large N gauge theories in 2+1 dimensions, dual to Sasaki-Einstein compactifications of M theory, towards 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 one milliVolt, we find critical temperatures ranging between 0.24 and 165 degrees Kelvin.