Probing the singularity at the holographic screen via $q$-holography

TL;DR

This paper investigates how $q$-deformed spacetime geometries emerge in a 2D dilaton gravity model with a singular boundary, revealing $q$-deformed symmetries through probe analysis and correlators, suggesting a $q$-deformed holographic duality.

Contribution

It demonstrates the emergence of $q$-deformed hyperbolic geometries in a 2D gravity model and connects this to $q$-deformed holographic duality, extending the understanding of $q$-deformations in holography.

Findings

$q$-deformed hyperbolic disk isometries observed in correlators

Singular boundary geometry influences the emergence of $q$-deformed symmetries

Potential extension to DSSYK and sine dilaton gravity models

Abstract

We study the emergence of $q$-deformed spacetime in a lower-dimensional gravitational system whose asymptotic region geometrizes the global symmetry of a $q$-deformed CFT. More precisely, we consider the 2d sinh dilaton gravity model, whose classical metric solutions exhibit a curvature singularity at the holographic boundary. Our aim is to probe this UV near-boundary regime by injecting a small probe into the bulk, and identifying the geometrical features it observes. At the level of the two-point correlator, we see the emergence of $q$-deformed hyperbolic disk isometries. By formulating DSSYK in terms of the analogous sine dilaton gravity model, we expect this $q$-deformed holographic duality to persist.