Holographic superconductivity in M-Theory

TL;DR

The paper embeds holographic superconductivity in three spacetime dimensions within a string/M-theory framework by using a consistent KK truncation of $D=11$ supergravity on seven-dimensional Sasaki-Einstein spaces $SE_7$. It derives a 4D effective action with a real scalar and a gauge field whose solutions uplift to full $D=11$ backgrounds, and studies electrically charged black holes that develop scalar hair below a critical temperature $T_c \sim 0.042$, forming a superconducting phase. Thermodynamics is analyzed via the on-shell action, with a Smarr relation and first law confirming consistency, and numerical results show a zero-temperature limit in which the geometry flows to a charged domain wall between two $AdS_4$ vacua, indicating a quantum critical point with vanishing entropy. These results extend holographic superconductivity beyond phenomenological models, offering a string/M-theory realization and suggesting avenues for incorporating magnetic charge and stability analyses.

Abstract

Using seven-dimensional Sasaki-Einstein spaces we construct solutions of D=11 supergravity that are holographically dual to superconductors in three spacetime dimensions. Our numerical results indicate a new zero temperature solution dual to a quantum critical point.

Figures (3)

• Figure 1: Plot showing $-\tfrac{1}{2} Gm$ (proportional to the thermodynamic potential $\Omega(T,\mu)$) against $T$ with fixed $\hat{\mu} = 1$, for unbroken phase solutions (long dashed red), broken phase (blue) and solutions of H32 (with their $L=1/2$ and their $q=2$) (dashed blue).
• Figure 2: Plot showing the asymptotic value of the scalar condensate, $(8\pi G)^{1/4}\sqrt{\sigma_2}$, against $T$ (conventions as above).
• Figure 3: Plots showing the value of the Ricci scalar (heavy lines) and $\sqrt{R_{\alpha\beta\mu\nu}R^{\alpha\beta\mu\nu}}$ (light lines) at the horizon normalized by $-64$ and $32$ respectively. (conventions as above).