Competing orders in M-theory: superfluids, stripes and metamagnetism

TL;DR

The paper develops a top-down holographic framework for a broad class of d=3 CFTs dual to skew-whiffed AdS4×SE7, focusing on finite T, chemical potential, and magnetic field. It constructs and analyzes dyonic black holes and their zero-temperature domain-wall limits within a four-dimensional Einstein-Maxwell-pseudoscalar truncation, revealing IR AdS2×R2 fixed points and emergent hyperscaling-violating behavior with $z=\tfrac{3}{2}$ and $\theta=-2$. The authors show a competition between superfluid and striped instabilities under a magnetic field, uncover a first-order metamagnetic transition at large $B$, and map out a rich phase diagram with paramagnetic and diamagnetic domains and HSV ground states. These results illuminate how magnetic field tunes holographic orders and stabilize complex ground states with potential analogies to metamagnetic materials, while highlighting avenues for fully backreacted, zero-temperature phases.

Abstract

We analyse the infinite class of d=3 CFTs dual to skew-whiffed AdS_4 X SE_7 solutions of D=11 supergravity at finite temperature and charge density and in the presence of a magnetic field. We construct black hole solutions corresponding to the unbroken phase, and at zero temperature some of these become dyonic domain walls of an Einstein-Maxwell-pseudo-scalar theory interpolating between AdS_4 in the UV and new families of dyonic AdS_2 X R^2 solutions in the IR. The black holes exhibit both diamagnetic and paramagnetic behaviour. We analyse superfluid and striped instabilities and show that for large enough values of the magnetic field the superfluid instability disappears while the striped instability remains. For larger values of the magnetic field there is also a first-order metamagnetic phase transition and at zero temperature these black hole solutions exhibit hyperscaling violation in the IR with dynamical exponent z=3/2 and θ=-2.

Figures (11)

• Figure 1: A schematic figure of a plausible phase diagram as a function of applied magnetic field. The solid lines denote second order phase transitions and the dashed lines first order. The two solid dots denote tri-critical points and the open circle a second order critical point where the metamagnetic transition ends. The phase diagram is symmetric under $B\to -B$. For $B>B_{(ii)}$ as $T\to 0$ the solutions exhibit hyperscaling violation in the IR with $z=3/2$ and $\theta=-2$.
• Figure 2: Two families of dyonic $AdS_2\times \mathbb{R}^2$ solutions. The left and right panels display the dependence of $E$ and $B$ on the value of the pseudo-scalar $\sigma$, respectively. For convenience of presentation we use $\tanh(\sigma/\sqrt{3})$ for the horizontal axis. The blue line is the electric family which contains a purely electric solution and the red line is the magnetic family which contains a purely magnetic solution. There are two more families of solutions obtained by simultaneously flipping the signs of $E,B$.
• Figure 3: Left panel: the one parameter family of domain wall solutions interpolating between $AdS_4$ in the UV, with deformation data $(\mu,B)$, and dyonic $AdS_2\times\mathbb{R}^2$ solutions in the electric family in the IR, labelled by $\sigma_0$. For convenience of presentation the vertical axis is given by $\tanh(\sigma_0/\sqrt{3})$. There can be two domain wall solutions for given $(\mu,B)$ and the upper branch has smaller free energy and is thermodynamically preferred. It is expected that the lower branch continues down to $B/\mu^2\to 0$. The red dots indicate superfluid instabilities, discussed in section \ref{['secsfluid']}, with the solutions being unstable to the left of the dots. Right panel: a plot of the magnetisation $m/\mu$ as a function of $B/\mu^2$. Observe that the magnetisation is always positive corresponding to paramagnetism.
• Figure 4: Left panel: the one parameter family of domain wall solutions interpolating between $AdS_4$ in the UV, with deformation data $(\mu,B)$, and dyonic $AdS_2\times\mathbb{R}^2$ solutions in the magnetic family in the IR, labelled by $\sigma_0$. For convenience of presentation the vertical axis is given by $\tanh(\sigma_0/\sqrt{3})$. It is expected that these domain walls exist for $B/\mu^2\to 0$ but that they have higher free energy than the domain walls in figure \ref{['dwallfig']} for the same values of $B,\mu$. The red dots indicate superfluid instabilities, discussed in section \ref{['secsfluid']}, with the solutions being unstable to the left of the crosses. Right panel: a plot of the magnetisation $m/\mu$ as a function of $B/\mu^2$. Observe that the magnetisation is always negative corresponding to diamagnetism.
• Figure 5: A representative plot of the free energy of two families of dyonic black hole solutions that exist in region I i.e. for values of $B/\mu^2$ with $0<B/\mu^2<(B/\mu^2)_I$. At $T=0$ each family approaches a smooth domain wall solution interpolating between $AdS_4$ in the UV and two different dyonic $AdS_2\times\mathbb{R}^2$ solutions in the IR. Notice that only the bottom branch can be heated up to arbitrarily high temperatures; it is thermodynamically preferred and describes the unbroken phase.