AI 中文总结
本文从全息视角，通过将四维规范超引力几何提升至高维，研究了全息对偶于三维$\text{N}=2$ SCFT ABJM模型的带电黑洞膜的费米子响应、谱隙及相关性质。
AI 中文摘要
我们研究四维规范超引力的$U(1)^4$带电黑洞膜解，并分析该几何中的费米子响应，其全息对偶于三维$\boldsymbol{\text{N}=2}$超共形场论ABJM模型。与\textit{DeWolfe:2013fha}类似，我们证明该共形场论的态中存在一个谱隙，对应四荷几何的两个不等化学势的不同极限行为。我们通过以不同阶改变理论参数，研究该谱隙的行为以及近地平线几何的稳定性。随后我们对该几何的56个费米子模式进行分类，求出每个模式的狄拉克方程系数，并评述狄拉克方程解在不同近地平线极限下的行为。接着我们将该几何提升到五维，再提升到十一维，且与\textit{Fareghbal:2008dy}类似，我们证明两种情况下都会出现一块$\boldsymbol{\text{BTZ} \times \text{S}^2}$或$\boldsymbol{\text{AdS}^3 \times \text{R}^2}$，因此场论中存在一个退耦部分。我们研究了这些提升几何中四维近地平线几何的奇点与前述谱隙。
英文摘要
We study the $U(1)^4$ charged black brane solution of four-dimensional gauged supergravity and analyze the fermionic response in this geometry, which is holographically dual to $3d$ $\mathcal{N}=2$ SCFT ABJM models. Similar to \cite{DeWolfe:2013fha}, we show that a gap exists in the states of the conformal field theory, which corresponds to the different limiting behaviors of the two unequal chemical potentials of the four-charge geometry. We study the behavior of this gap and also the stability of the near-horizon geometry by changing the parameters of the theory in various orders. We then categorize the $56$ fermion modes of the geometry, find the coefficients of the Dirac equations for each mode, and comment on the behavior of the solution of the Dirac equation in different near-horizon limits. We then uplift the geometry to five-dimensional and then to eleven-dimensional geometries and, similar to \cite{Fareghbal:2008dy}, we show that in both cases, a piece of $\mathrm{BTZ} \times \mathrm{S}^2$ or $\mathrm{AdS}^3 \times \mathbb{R}^2$ emerges, and as a result, a decoupling sector in the field theory exists. We study the singularity of the near-horizon $4d$ geometry and the mentioned gap in these uplifted geometries.
Comments36 pages, 7 figures
