Landscape of superconducting membranes

TL;DR

This paper explores the stability of certain supersymmetric gauge theories in 2+1 dimensions and demonstrates their tendency to become superconducting at finite chemical potential, with a range of critical temperatures.

Contribution

It identifies instabilities in charged black holes within M-theory compactifications, linking string theory landscapes to superconductivity phenomena.

Findings

Many theories exhibit charged operator condensation at finite chemical potential.

Critical temperatures for superconductivity range from 0.24K to 165K.

Statistical distribution of critical temperatures is computed for selected theories.

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 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.