2+1维de Sitter时空中的双曲型超材料与大质量Klein-Gordon方程
Hyperbolic Metamaterials and Massive Klein-Gordon Equation in 2+1 Dimensional de Sitter Spacetime
摘要：
双曲超材料中电场的非寻常分量所服从的波动方程被证明是一个无质量的克莱因-戈登场，它存在于具有两个类时和两个类空维的平坦时空中。出乎意料的是，这样的波动方程允许无色散传播，尽管具有两个空间维度。在这里，我们表明，同样的方程可以很自然地解释为一个特殊的大质量克莱因-戈登方程与通常的一个类时和两个类空维在德西特（dS）的背景时空。标量场的质量参数由宇宙学常数、普朗克常量和光速表示为$m =\sqrtΛ\frac{\hbar}{c}$，它对应于边界共形场论（CFT）（通过德西特/CFT对应）的左右共形权相等的点。这个特定的质量对应于dS时空中的无隙模式，其色散关系在波数上是线性的。
英文摘要：
The wave equation obeyed by the extraordinary component of the electric field in a hyperbolic metamaterial was shown to be a massless Klein-Gordon field living in a flat spacetime with two timelike and two spacelike dimensions. Such a wave equation, unexpectedly, allows dispersionless propagation albeit having two spatial dimensions. Here we show that the same equation can be naturally interpreted as a particular massive Klein-Gordon equation with the usual one timelike and two spacelike dimensions in a de Sitter (dS) background spacetime. The mass parameter of the scalar field is given in terms of the cosmological constant, Planck constant and the speed of light as $m =\sqrtΛ\frac{\hbar}{c}$ which corresponds to the point for which the left and right conformal weights of the boundary conformal field theory (CFT) (via the de Sitter/CFT correspondence) are equal. This particular mass corresponds to the gapless mode in the dS spacetime for which the dispersion relation is linear in the wave number.
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