朗道能级、各向异性与全息
Landau Levels, Anisotropy and Holography
摘要：
我们分析了具有各向异性近视界几何的（4+1）维极端黑膜对偶场论的性质。这种引力解最近被证明可以分为九类，与实三维李代数的比安奇分类相一致。作为热身，我们计算的能量条件下的散装和标量两点函数的一般I型度量，它具有平移不变性，但破碎的旋转临界指数的约束。我们还评论的分歧性质的潮汐力一般Bianchi型度量。然后，我们来到我们的主要焦点：极值膜，其近视界等距是海森堡代数（II型）。在（4+1）维中我们发现了具有II型等距的超标度破坏解。通过Kaluza-Klein约化，我们证明了尺度不变的（4+1）维II型度量与更对称的$AdS_2\times R^2$和（3+1）维超标度违反时空有关.这些溶液通常含有$θ\leq 0$。我们讨论了如何通过希格斯机制，以及潜在的II型非均匀不稳定性，可以获得流从UV CFTs Bianchi型时空在IR。最后，我们计算了对偶场论中有质量和无质量标量算符的两点函数，发现它们表现出朗道能级理论的行为。
英文摘要：
We analyze properties of field theories dual to extremal black branes in (4+1) dimensions with anisotropic near-horizon geometries. Such gravity solutions were recently shown to fall into nine classes which align with the Bianchi classification of real three-dimensional Lie algebras. As a warmup we compute constraints on critical exponents from energy conditions in the bulk and scalar two point functions for a general type I metric, which has translation invariance but broken rotations. We also comment on the divergent nature of tidal forces in general Bianchi-type metrics. Then we come to our main focus: extremal branes whose near-horizon isometries are those of the Heisenberg algebra (type II). We find hyperscaling-violating solutions with type II isometries in (4+1)-dimensions. We show that scale invariant (4+1)-dimensional type II metrics are related by Kaluza-Klein reduction to more symmetric $AdS_2\times R^2$ and (3+1)-dimensional hyperscaling-violating spacetimes. These solutions generically have $θ\leq 0$. We discuss how one can obtain flows from UV CFTs to Bianchi-type spacetimes in the IR via the Higgs mechanism, as well as potential inhomogeneous instabilities of type II. Finally, we compute two-point functions of massive and massless scalar operators in the dual field theory and find that they exhibit the behavior of a theory with Landau levels.
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