Is Action Complexity better for de Sitter space in Jackiw-Teitelboim gravity?

Abstract

Volume complexity in dS${}_2$ remains $O(1)$ up to a critical time, after which it suddenly diverges. On the other hand, for the dS${}_2$ solution in JT gravity there is a linear dilaton which smoothly grows towards the future infinity. From the dimensional reduction viewpoint, the growth of the dilaton is due to the expansion of the orthogonal sphere in higher-dimensional dS${}_d$ ($d\ge 3$). Since in higher dimensions complexity becomes very large even before the critical time, by properly taking into account the dilaton, the same behavior is expected for complexity in dS${}_2$ JT gravity. We show that this expectation is met by complexity = action (CA) conjecture. For this purpose, we obtain an appropriate action for dS${}_2$ in JT gravity, by dimensional reduction from dS${}_3$. In addition, we discuss complexity = "refined volume" where we choose an appropriate Weyl field-redefinition such that refined volume avoids the discontinuous jump in time evolution.

v2, 30 pages, 3 figures, minor typos corrected, references added

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• Generalized holographic complexity of rotating black holes
• The Complexity of Being Entangled
• Jackiw-Teitelboim Gravity and Lorentzian Quantum Cosmology
• Entanglement Entropy and Complexity in Dyonic Quantum Black Holes