22-24 May 2023
Europe/Madrid timezone

A bulk manifestation of Krylov complexity

23 May 2023, 10:30


Adrián Sánchez Garrido


The double-scaled SYK (DSSYK) model provides an analytically tractable instance of low-dimensional holography in which the existence of an expansion in terms of chord diagrams allows for an explicit construction of both the bulk Hilbert space and the Hamiltonian of JT gravity from the boundary theory. In this talk, I will present recent results that build up on this framework and propose a precise entry for Krylov complexity in the holographic dictionary. I will show that the eigenstates of the Krylov complexity operator are identified with the fixed chord number states that build up the effective Hilbert space of DSSYK, therefore providing bulk length eigenstates once they are subject to the bulk/boundary map. This allows to compute the profile of bulk length as a function of time in terms of the boundary K-complexity. For the sake of completeness, a concise review on the necessary notions of K-complexity will also be provided.

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