Sergio Aguilar - Pushing boundaries with the double-scaled SYK model

Sergio Ernesto Aguilar Gutierrez (KU Leuven): Pushing boundaries with the double-scaled SYK model: TTbar deformations, thermodynamics, and Krylov complexity

Explicit examples of the holographic duality outside the anti-de Sitter (AdS) space/conformal field theory (CFT) correspondence are relatively scarce and, arguably, not well-understood. However, low-dimensional quantum gravity allows new opportunities to explore holography for geometries with different metrics and asymptotic boundary conditions with respect to AdS space. In particular, the double scaled SYK model (DSSYK) has catalyzed new developments in non-AdS holography, as its dual bulk geometry contains regions of both positive and negative Ricci curvature, having both black hole and cosmological horizons; and is described by a dilaton-gravity theory with a Sin Phi. We study TTbar-deformations in the DSSYK model after performing the ensemble averaging to probe the thermodynamics and quantum information observables associated with the regions of positive curvature, which allows for an approximate description of 2-dimensional de Sitter (dS) space with an explicit quantum mechanical model at arbitrary high energies. We study the structure of the Hilbert space of the deformed DSSYK model, and transfer matrix using the finite cutoff interpretation of the TTbar-deformation. By placing the DSSYK model in the stretched horizon of the dual geometry with a positive and nearly constant scalar curvature, we realize the stretched horizon proposal of Susskind. We evaluate the conditions for the energy spectrum of the deformed system to be well defined, and for the system to be thermodynamically stable. We study quantum information properties of the deformed model, including Krylov complexity for states and operators, and entanglement entropy for a bipartition of the system, which show close similarity with those expected in stretched horizon holography.