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arXiv · 2606.31705

Monitoring a de Sitter universe through an anti-de Sitter window

Sarah Hoback·Daniel L. Jafferis·Zixia Wei
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Abstract

We propose that AdS$_3$ gravity coupled to dS$_2$ end-of-the-world branes is dual to a unitary holographic CFT$_2$ with non-unitary conformal boundary conditions. These boundary conditions have complex $g$-functions and appear in conjugate pairs. The associated gravitational path integral admits no real saddles, but does admit complex saddles. We show that an AdS$_3$ black hole microstate with a dS$_2$ brane behind the horizon corresponds to the unitary time evolution of a pure CFT state prepared by a Euclidean path integral on a cylinder with such boundary conditions. The construction predicts a boundary-condition-changing primary with $h=-c/8$, which resides in the boundary sector rather than the bulk spectrum and is therefore compatible with unitarity of the underlying CFT. This realizes dS holography as state preparation in a unitary AdS/CFT Hilbert space.

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Sarah Hoback, Daniel L. Jafferis, Zixia Wei. 2026-06-30. Monitoring a de Sitter universe through an anti-de Sitter window. https://arxiv.org/abs/2606.31705

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