# Quantum Criticality and Holographic Superconductors in M-theory

## TL;DR

This paper develops a supergravity model in four dimensions derived from eleven-dimensional M-theory, constructing black hole solutions that reveal complex phase behavior including holographic superconductivity and emergent conformal symmetry at zero temperature.

## Contribution

It introduces a new consistent Kaluza-Klein truncation of D=11 supergravity on Sasaki-Einstein spaces, enabling the study of holographic superconductors with broken symmetries.

## Key findings

- Identification of a rich phase diagram with superconducting phases
- Construction of charged domain walls with emergent conformal symmetry
- Demonstration of broken parity and time-reversal invariance in dual CFTs

## Abstract

We present a consistent Kaluza-Klein truncation of D=11 supergravity on an arbitrary seven-dimensional Sasaki-Einstein space (SE_7) to a D=4 theory containing a metric, a gauge-field, a complex scalar field and a real scalar field. We use this D=4 theory to construct various black hole solutions that describe the thermodynamics of the d=3 CFTs dual to skew-whiffed AdS_4 X SE_7 solutions. We show that these CFTs have a rich phase diagram, including holographic superconductivity with, generically, broken parity and time reversal invariance. At zero temperature the superconducting solutions are charged domain walls with a universal emergent conformal symmetry in the far infrared.