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Résumé |
Within the framework of the AdS/CFT correspondence, the time dynamics of black holes in the bulk hints to the existence of boundary observables that evolve for very long time-scales. The search for such boundary observables yielded several notions of quantum complexity, though a precise and direct bulk-boundary correspondence was lacking. In this talk we focus on a particular notion of quantum complexity, known as Krylov complexity. We will provide a pedagogical overview, including some interesting results, for this boundary observable, and show how to work with it in the case of double-scaled SYK. Finally, we will show that in the limit where double-scaled SYK is dual to JT gravity, Krylov complexity evolving in time on the boundary has a precise gravitational description in the bulk. |
