Hyperbolic metamaterials and massive Klein-Gordon equation in (2+1)-dimensional de Sitter spacetime

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 = root Lambda(h) over bar /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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Citation Formats
B. Tekin, “Hyperbolic metamaterials and massive Klein-Gordon equation in (2+1)-dimensional de Sitter spacetime,” PHYSICAL REVIEW D, vol. 104, no. 9, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/94912.