Near-extremal membranes in M-theory

TL;DR

This work analyzes the perturbative stability of near-extremal membranes in M-theory, realized via a consistent truncation to ${\cal N}=2$ gauged supergravity on $M^{1,1,0}$ and holographically dual to a 2+1D SCFT with $U(1)_R\times U(1)_B$. By constructing baryonic and $R$-charged black membranes and examining linearized fluctuations, the authors identify three near-extremal regimes and show that baryonic backgrounds are perturbatively stable while $R$-charged backgrounds lack superconducting instabilities but exhibit diffusion-driven transport instabilities and axion-related fluctuations, with the precise behavior depending on normal vs alternative quantization of bulk modes. The RN (R-charged) membrane analysis reveals a positive $R$-charge diffusion coefficient across parameter ranges, but a negative diffusion for baryonic transport below a critical temperature, indicating a baryonic clumping instability that precedes any neutral-axion condensation. Collectively, the results provide a concrete, perturbatively stable non-supersymmetric extremal horizon in string/M-theory within the KPT/KCV framework and highlight how topological versus non-topological charges shape stability and potential phase structure in holographic 2+1D quantum critical systems.

Abstract

We consider near-extremal membranes embedded in M-theory, consistently truncated to gauged $\mathcal{N} = 2$ supergravity in four dimensions on the coset space $M^{1,1,0}$. These are holographically dual to $2 + 1$ dimensional superconformal gauge theory with $U(1)_R \times U(1)_B$ global symmetry. Turning on the chemical potential to either the $R$-symmetry or the baryonic symmetry gives access to the quantum critical regime of the boundary gauge theory. We study perturbative stability of the extremal limit, and demonstrate that membranes with topological (baryonic) charge are free from all known instabilities. $R$-charged membranes are free from the superconducting instabilities, but have unstable charge transport and instabilities associated with the condensation of the axions.

Figures (7)

• Figure 1: The values of the bulk scalars $v_1$ and $v_2$ at the horizon for different quantizations of the mode $\ln[v_1v_2^{-1}]$ (see table \ref{['table1']}): ${\cal O}_2$ (black) and ${\cal O}_1$ (blue). The limit $q/q_{crit}\to 1$ is a quantum critical regime corresponding to the zero-temperature limit $T\to 0$ of the baryonic black membranes \ref{['sol2']} and \ref{['so2ir']}; the regime $q/q_{crit}\to 0$ is the black membrane solution with vanishing baryonic charge density --- the $AdS_4$-Schwarzschild background with the trivial profile for the scalars $v_1=v_2\equiv 1$\ref{['sol1']}.
• Figure 2: The values of the bulk scalar $g$ at the horizon and the reduced temperature $T/\alpha$ (see \ref{['tbaryonic']}) for different quantizations of the mode $\ln[v_1v_2^{-1}]$ (see table \ref{['table1']}): ${\cal O}_2$ (black) and ${\cal O}_1$ (blue). The limit $q/q_{crit}\to 1$ is a quantum critical regime corresponding to $T\to 0$ of the baryonic black membranes \ref{['sol2']} and \ref{['so2ir']}; the regime $q/q_{crit}\to 0$ is the black membrane solution with vanishing baryonic charge density --- the $AdS_4$-Schwarzschild background with the trivial profile for the scalar $g\equiv 1$\ref{['sol1']}.
• Figure 3: $R$-charge dimensionless diffusion coefficient ${\cal D}_R=2\pi T D$ of the baryonic membrane theory plasma for different quantizations of the gravitational dual (pseudo)scalars $\{\ln[v_1v_2^{-1}],b_1-b_2\}$: $\{{\cal O}_2,\delta{\cal O}_2^b\}$ (black,solid), $\{{\cal O}_2,\delta{\cal O}^b_1\}$ (black,dashed), $\{{\cal O}_1,\delta{\cal O}_2^b\}$ (blue,solid), $\{{\cal O}_1,\delta{\cal O}^b_1\}$ (blue,dashed). At $q=0$, ${\cal D}_R=\frac{3}{2}$\ref{['an3']}, while it vanishes in the quantum critical regime $q\to q_{crit}$, correspondingly $T\to 0$.
• Figure 4: We test the instability of the baryonic black membranes due to the condensation of the neutral $(b_1-b_2)$ mode: the instability would be signaled by the divergence of the response of the corresponding operator for its fixed source, as we vary $q/q_{crit}$. The color coding is as in fig. \ref{['figure3']}.
• Figure 5: Dimensionless baryonic charge diffusion coefficient ${\cal D}_B=2\pi T D$ of the $R$-charged membrane theory plasma for different quantizations of the gravitational dual pseudoscalar $(b_1-b_2)$: $\{\delta{\cal O}_2^b\}$ (black), $\{\delta{\cal O}^b_1\}$ (blue). The vertical red lines indicate the onset of the baryonic charge clumping instability, see \ref{['tcritb']}.