Abstract
We further explore the quantum dynamics near past cosmological singularities in anisotropic Kasner-AdS solutions using gauge/gravity duality. The dual description of the bulk evolution involves $$ \mathcal{N}=4 $$ super Yang-Mills on the contracting branch of an anisotropic de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlator between two points separated in a direction with negative Kasner exponent p always exhibits a pole at horizon scales, in any dimension, which we interpret as a dual signature of the classical bulk singularity. This indicates that the geodesic approximation selects a non-normalizable Yang-Mills state.
Highlights
Boundary it remains everywhere well defined [10, 11]
The existence of such geodesics probing the high curvature region near the singularity in Kasner-AdS opens up the possibility of using the dual conformal field theory to study the quantum dynamics near singularities
We have found an example of a cosmological singularity with a well defined holographic dual
Summary
Where we have set the AdS radius to 1. We use the geodesic solutions for general p of the previous section to argue that the two-point correlator separated in a direction with negative Kasner exponent p, for any negative value of p and any spacetime dimension, will feature a pole at the cosmological horizon. Including only one of the real geodesics for values of Lbdy below the merger point would result in a discontinuity in the correlator at some length scale larger than the horizon This unphysical result strongly suggests that both real geodesics contribute and the pole at the horizon is physical. Subtracting the divergent pure AdS contribution 2 ln and neglecting O( ) contributions yields the two-point correlator along the p = −1/2 direction This correlator has precisely two points of divergence: c = −1, corresponding to the usual short-distance singularity ∼ 1/L2b∆dy and c = 0, corresponding to the null boundary geodesic at horizon separation ∼ 1/(Lbdy − Lhor)∆. This holds in all cases we can check, but we do not yet have a general derivation
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