Quantum Criticality and Holographic Superconductors in M-theory

TL;DR

The authors construct a robust, top-down holographic framework by deriving a consistent four-dimensional KK truncation of eleven-dimensional supergravity on Sasaki-Einstein seven-manifolds, yielding a theory with a metric, a gauge field, a charged scalar and a neutral scalar. They use this setup to uncover a rich phase structure in the dual 3D CFTs, including holographic superconductivity with parity and time-reversal breaking and an emergent conformal symmetry in the infrared at zero temperature. The phase diagram, featuring unbroken and superconducting phases and transitions between AdS4 and AdS2 IR geometries, is explored through charged/uncharged black holes and domain-wall solutions, with detailed thermodynamics and conductivity computations. The results provide a concrete M-theory realization of quantum critical superconductivity, including a universal IR fixed point in the superconducting phase and a concrete setup for studying stability and future extensions across Sasaki-Einstein manifolds.

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.

Figures (16)

• Figure 1: The phase diagram for the holographic superconductors. The vertical axis is temperature, the horizontal axis determines the deformation of the skew-whiffed CFT by the operator ${\cal O}_h$ and the chemical potential $\mu$ is non-zero.
• Figure 2: The plot shows the scalar potential of our model in the $(h,\xi)$ plane. The extrema indicated by dots correspond to the skew-whiffed $AdS_4$ vacuum (SW), the Pope-Warner vacuum (PW) and the Englert vacuum (E). The interpolating trajectories are domain wall solutions that describe holographic flows interpolating between a deformed skew-whiffed vacuum in the UV and a Pope-Warner vacuum in the IR.
• Figure 3: Plot showing the behaviour of $h_2$ and $\xi_2$ as a function of $h_1$ in the uncharged domain wall solutions.
• Figure 4: Plot in the $(h,\xi)$ plane showing the interpolating trajectories of the charged domain wall solutions interpolating between the skew-whiffed vacuum in the UV and the Pope-Warner vacuum in the IR. Along the trajectories $\phi\neq0$.
• Figure 5: Plots showing $h_2$, $\xi_2$ and $q$ for the one-parameter family of charged domain wall solutions labelled by $h_1$ with $(16\pi G)^{1/2} \mu=1$.