On stability of baryonic black membranes

TL;DR

This work analyzes the stability of near-extremal baryonic membranes in M-theory on $M^{1,1,0}$, realized as a ${\mathbb Z}_2$-invariant sector of the $Q^{1,1,1}$ compactification. By focusing on the ${\mathbb Z}_2$-odd fluctuations in the larger truncation, it shows that a bulk scalar dual to a boundary operator with dimension $Δ=1$ can trigger a dynamical instability in the off-diagonal ${U(1)}_{B,-}$ charge transport, yielding a negative diffusion coefficient $D_{B,-}$ below a critical temperature. The diffusion behavior depends crucially on the quantization of the ${\cal O}_-$ operator: $Δ=2$ (normal quantization) keeps $D_{B,-}>0$ for all $T$, while $Δ=1$ (alternative quantization) produces a ${U(1)}_{B,-}$-clumping instability at low $T/μ_B$. Additionally, a homogeneous threshold instability from condensing ${\delta v_-}, {\delta b_-}$ is not found, implying no homogeneous ${\mathbb Z}_2$-breaking phase in this sector. Together, these results delineate the stability landscape of baryonic membranes and highlight the role of operator dimension and quantization in holographic transport instabilities.

Abstract

Near-extremal black membranes with topological (baryonic) $U(1)_B$ charge of M-theory compactified on the coset space $M^{1,1,0}$ are stable. $M^{1,1,0}$ coset is a ${\mathbb Z}_2$-invariant truncation of a larger $Q^{1,1,1}$ coset, with diagonal $U(1)_B\equiv U(1)_{B,+}\subset U(1)_B^2$ symmetry of the latter. We show that the baryonic black membranes of M-theory $M^{1,1,0}$ compactifications are unstable to ${\mathbb Z}_2$-odd gravitational bulk gauge and scalar fluctuations, but only if this bulk scalar is identified with the holographically dual $2+1$ dimensional superconformal gauge theory operator of conformal dimension $Δ=1$. The instability is associated with the unstable charge transport of the off-diagonal $U(1)_{B,-}\subset U(1)_B^2$ symmetry.

Figures (1)

• Figure 1: $U(1)_{B,-}$-charge dimensionless diffusion coefficient ${\cal D}_{B,-}=2\pi T D_{B,-}$ of the baryonic membrane theory plasma for different quantizations of the gravitational dual scalars $\{\ln[v_1v_2^{-1}],\delta \ln[v_1v_3^{-1}]\}$: $\{{\cal O}_2,\delta{\cal O}_2^{\cal V}\}$ (black,solid), $\{{\cal O}_2,\delta{\cal O}^{\cal V}_1\}$ (black,dashed), $\{{\cal O}_1,\delta{\cal O}_2^{\cal V}\}$ (blue,solid), $\{{\cal O}_1,\delta{\cal O}^{\cal V}_1\}$ (blue,dashed). At $q=0$, ${\cal D}_{B,-}=\frac{3}{2}$\ref{['an3']}, while it vanishes in the quantum critical regime $q\to q_{crit}$, ${\cal D}_{B,-}\propto \frac{T}{\mu_B}\to 0$. Independent of the background scalar $\ln[v_1v_2^{-1}]$ quantization, there is an onset of the $U(1)_{B,-}$ charge clumping instability for $\delta \ln[v_1v_3^{-1}]\Longleftrightarrow \delta{\cal O}_1^{\cal V}$ quantization (the dashed curves), represented by vertical red lines.