arXiv subjects

Damiano Tietto

Publications and source records attributed to Damiano Tietto.

3 recordsLinked to original sources

arXiv2026

An observer's quantization of 3d de Sitter

What is the density of states of the de Sitter static patch? We propose a definition and calculation of such a density in 3d dS. Our proposal involves a sum over an SL(2,$\mathbb{Z}$) set of Euclidean no-boundary Kerr-lens spacetimes sourced by a line-defect with given energy and spin - which in Lorentzian time represents an observer's worldline at the center of the dS static patch. We develop an exact quantum computation of the spectral density using a holographic duality between dS$_3$ gravity and two copies of $\mathbb{C}$LS, the complex Liouville string. The SL(2,$\mathbb{Z}$) Kerr-lens spacetimes map under the duality to an SL(2,$\mathbb{Z}$) family of generalized crosscap geometries. We compute the $\mathbb{C}$LS $\otimes$ $\mathbb{C}$LS crosscap amplitudes and show that they match the semi-classical gravity prediction. For the simplest non-trivial Kerr-lens space, the $\mathbb{C}$LS $\otimes$ $\mathbb{C}$LS description is, in turn, dual to two copies of the $GΣ$ effective field theory of the double scaled SYK model. The $GΣ\otimes GΣ$ theory lives on an observer's worldline in the static patch, setting the stage for developing a microscopic worldline hologram of 3d de Sitter.

hep-th↗

arXiv2025

SYK collective field theory as complex Liouville gravity

We establish a precise relationship between the $GΣ$ collective field theory of the double scaled SYK model and the worldsheet theory of the complex Liouville string a.k.a. sine dilaton gravity. The relationship is similar to the lightcone gauge in critical string theory, and to what transpires when we gravitationally dress to an observer in gravity: one of the Liouville fields plays the role of a dynamical clock with respect to which the second Liouville field evolves. This other Liouville field is identified with the collective field of SYK, which thus acquires a direct gravity interpretation. The relevant 2D worldsheet geometry is that of a disk with specific crosscap and FZZT boundary conditions, as deduced from the $GΣ$ formulation. We compute the CLS amplitude on this geometry and find that this coincides with the DSSYK partition function. We indicate how our results can be lifted to 3D gravity, previewing upcoming work. An outflow of our results is that physical operators of DSSYK are mapped to holonomy operators (Verlinde lines) of complex Liouville theory on the crosscap geometry, which in turn have a 3D representation in terms of line operators in 3D de Sitter gravity. We show that the partition function of SYK can be represented as the expectation value of a circular gravitational Wilson line on $\mathbb{RP}^3$ (a.k.a. elliptic 3D de Sitter space).

hep-th↗

arXiv2025

A microscopic model of de Sitter spacetime with an observer

We introduce a simple microscopic quantum mechanical model of low-dimensional de Sitter holography with an observer. Using semiclassical gravity and elementary thermodynamic considerations, we derive a formula for the total entropy of a 3D Schwarzschild-de Sitter universe with an observer. We then match this entropy formula with the exactly known spectral density of the double scaled SYK model. Our result gives a de Sitter interpretation of the appearance of two notions of temperature in DSSYK.

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