发表机构
IndigoWave, Center for Quantum Spacetime, Sogang University（IndigoWave，西江大学量子时空中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在AdS₄爱因斯坦-标量引力中，从单标量毛发黑洞膜微扰引入第二个标量，求解耦合系统至ε²阶，得到双标量毛发平面黑洞的相关闭式解，分析了对偶流体的输运系数与声速等性质。
AI 中文摘要
我们在四维爱因斯坦引力与两个标量耦合的框架下构造了一个双标量毛发平面黑洞，其势来自十一维超引力的ABJM一致约化。从已知的单标量毛发黑洞膜出发，我们按振幅ε微扰地开启第二个标量φ^m，并求解耦合的爱因斯坦-标量系统至ε²阶。线性化的φ^m剖面是精确的超几何函数，与φ^p毛发无关，其视界正则分支始终带有源，因此不存在自发的φ^m毛发。由于对偶算子O_-是无关的（标度维数Δ=4），二阶响应产生对数跑动的凝聚，其闭式、与方案无关的斜率为√21/70 C_s²。重整化自由能与方案相关，但固定熵下的几何温度偏移δT/T₀≈-0.345 ε²则与方案无关。我们得到了完整的度规和φ^p反作用的闭式解，将其对角化为两个Pöschl-Teller问题，满足δφ^p=6/√7 δH。对偶流体的三个输运系数在该阶仍保持共形性，而声速则与自由能一样与方案相关。
英文摘要
We construct a two-scalar hairy planar black hole in four-dimensional Einstein gravity coupled to two scalars whose potential descends from the ABJM consistent truncation of eleven-dimensional supergravity. Starting from the known single-scalar hairy black brane, we switch on the second scalar $\phim$ perturbatively in its dimensionless hair parameter $\eps$, which at fixed source is proportional to $λ_{-}T$, and solve the coupled Einstein-scalar system to order $\eps^{2}$. The linearized $\phim$ profile is an exact hypergeometric function, independent of the $\pp$ hair, whose horizon-regular branch always carries a source, so there is no spontaneous $\phim$ hair. Because the dual operator is irrelevant ($Δ_{-}=4$), the second-order response develops a resonant logarithm: the condensate runs with a closed-form coefficient fixed by the cubic vertex. The metric and $\pp$ back-reaction is obtained in closed form; for arbitrary hair it diagonalizes into two Pöschl-Teller problems and locks the $\pp$ correction to the transverse metric correction with ratio $6/\sqrt7$. On AdS-Schwarzschild the first law and holographic renormalization agree and give an analytic equation of state, $T/T_{0}-1=-\tfrac{5\sqrt3}{8π}\eps^{2}$ at fixed entropy and $c_{s}^{2}=\tfrac12-\tfrac{5\sqrt3}{8π}\eps^{2}$, with $η/s=1/4π$ and $ζ/η=\tfrac14\eps^{2}$. We then add the $\mathbb{Z}_{2}$-odd third scalar $χ$ of the truncation, dual to $Δ_χ=5$. On the hairy background its linear equation is a Heun equation with an apparent singularity, solved by a Clausen function. At second order $χ$ necessarily sources $\phim$, yet neither cross-coupling makes either condensate run, a mutual non-renormalization that follows from a one-step resonance identity and the relation $2Δ_χ-Δ_{-}=2d$.
Comments30 pages; v2: minor change; v3: sections and references added, several corrections
