Rindler-AdS/CFT

TL;DR

Addresses how acceleration horizons behave in quantum gravity by proposing a holographic duality between Rindler-AdS space and an entangled pair of boundary CFTs.The AdS3 setup allows explicit calculations of the bulk-boundary propagator, thermal boundary correlators, and entropy via the Cardy formula, reproducing the Rindler thermodynamics.The paper further shows that a boundary observer can gain partial information about events across the horizon through the pole structure of a boundary one-point function for an infalling bulk source, highlighting nonlocal aspects of holography.An alternative foliation yields a boundary theory on de Sitter space, suggesting connections to de Sitter holography and broader implications for horizon physics.

Abstract

In anti-de Sitter space a highly accelerating observer perceives a Rindler horizon. The two Rindler wedges in AdS_{d+1} are holographically dual to an entangled conformal field theory that lives on two boundaries with geometry R x H_{d-1}. For AdS_3, the holographic duality is especially tractable, allowing quantum-gravitational aspects of Rindler horizons to be probed. We recover the thermodynamics of Rindler-AdS space directly from the boundary conformal field theory. We derive the temperature from the two-point function and obtain the Rindler entropy density precisely, including numerical factors, using the Cardy formula. We also probe the causal structure of the spacetime, and find from the behavior of the one-point function that the CFT "knows" when a source has fallen across the Rindler horizon. This is so even though, from the bulk point of view, there are no local signifiers of the presence of the horizon. Finally, we discuss an alternate foliation of Rindler-AdS which is dual to a CFT living in de Sitter space.

Figures (4)

• Figure 1: Geometry of Rindler-AdS$_{d+1}$ space. A surface of constant $\xi$ is a $\mathbb{R} \times H_{d-1}$ hypersurface. $\tau$ and $\rho$ are the time and radius in global coordinates; except at $\rho = 0$ each point in the interior corresponds to a $S^{d-2}$. The Rindler-AdS region extends only up to $\tau = \pm \pi/2$ at the boundary of AdS. The arrow on the right points in the direction of $\partial_t$, whose orbits are a Rindler observer's worldline; the arrow is reversed for the antipodal observer. One copy of the CFT lives on the boundary within the region shown in red.
• Figure 2: The locus of points on the boundary where there are poles coming from one endpoint of the source trajectory. The specific values plotted are for the case where the source switches off precisely on the horizon, for which there are only $v$ poles coming from the intersection of the past light cone of the endpoint with the hypersurface on which the CFT lives.
• Figure 3: a) The left figure illustrates when the source is active for a certain time period outside the horizon in the right Rindler wedge (R). The red and blue lines indicate signals propagating towards the AdS boundary which correspond to the creation and annihilation of the source respectively. The four poles are indicated on the boundary where the CFT lives. b) The right figure shows a source that crosses the horizon. It is evident that the retarded signal from the annihilation (or switching off) of the source no longer reaches the CFT boundary, and therefore the CFT perceives just three poles as shown. The dashed lines indicate the boundary of the Eddington-Finkelstein coordinates.
• Figure 4: Geometry of Rindler-AdS$_{d+1}$ space. The shaded region is a surface of constant $R$, which covers the static patches of a pair of antipodal de Sitter observers. $\tau$ and $\rho$ are the time and radius in global coordinates. The Rindler-AdS region extends only up to $\tau = \pm \pi/2$ at the boundary of AdS. The arrow in the right shaded region points in the direction of $\partial_t$, whose orbits are a Rindler/de Sitter observer's worldline; the arrow is reversed for the antipodal observer. Except at $\rho = 0$ each point in the interior corresponds to a $S^{d-2}$.