Cosmology from confinement?

Abstract

We describe a class of holographic models that may describe the physics of certain four-dimensional big-bang / big-crunch cosmologies. The construction involves a pair of 3D Euclidean holographic CFTs each on a homogeneous and isotropic space $M$ coupled at either end of an interval $\mathcal{I}$ to a Euclidean 4D CFT on $M\times \mathcal{I}$ with many fewer local degrees of freedom. We argue that in some cases, when the size of $M$ is much greater than the length of $\mathcal{I}$, the theory flows to a gapped / confining three-dimensional field theory on $M$ in the infrared, and this is reflected in the dual description by the asymptotically AdS spacetimes dual to the two 3D CFTs joining up in the IR to give a Euclidean wormhole. The Euclidean construction can be reinterpreted as generating a state of Lorentzian 4D CFT on $M\times \mathrm{time}$ whose dual includes the physics of a big-bang / big-crunch cosmology. When $M$ is ${\mathbb{R}}^3$, we can alternatively analytically continue one of the ${\mathbb{R}}^3$ directions to get an eternally traversable four-dimensional planar wormhole. We suggest explicit microscopic examples where the 4D CFT is $\mathcal{N}=4$ SYM theory and the 3D CFTs are superconformal field theories with opposite orientation. In this case, the two geometries dual to the pair of 3D SCFTs can be understood as a geometrical version of a brane-antibrane pair, and the tendency of the geometries to connect up is related to the standard instability of brane-antibrane systems.

arXiv comment45 pages, 16 figures, v2: typos corrected

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