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A<sc>bstract</sc> We use a combination of analytical and numerical methods to study out-of-time order correlators (OTOCs) in the sparse Sachdev-Ye-Kitaev (SYK) model. We find that at a given order ofN, the standard result for theq-local, all-to-all SYK, obtained through the sum over ladder diagrams, is corrected by a series in the sparsity parameter,k. We present an algorithm to sum the diagrams at any given order of 1/(kq)ⁿ. We also study OTOCs numerically as a function of the sparsity parameter and determine the Lyapunov exponent. We find that numerical stability when extracting the Lyapunov exponent requires averaging over a massive number of realizations. This trade-off between the efficiency of the sparse model and consistent behavior at finiteNbecomes more significant for larger values ofN. 

A<sc>bstract</sc> We investigate the spectral form factor of the sparse Sachdev-Ye-Kitaev model. We use numerical methods to establish that at intermediate times the connected part of the spectral form factor is the dominant one. These connected contributions arise from fluctuations around the disconnected geometry, not from a new saddle point. A similar effect was previously conjectured in SYK but required a value ofNout of reach of current numerical simulations. 

A<sc>bstract</sc> We consider anisotropic black holes in the context of holographic renormalization group (RG) flows. We construct ana-function that is stationary at the boundary and the horizon and prove that it is also monotonic in both the exterior and the interior of the black hole. In spite of the reduced symmetry, we find that the “radial” null energy condition is sufficient to ensure the existence of this monotonica-function. After constructing thea-function, we explore a holographic anisotropicp-wave superfluid state as a concrete example and numerical testing grounds. In doing so, we find that thea-function exhibits nontrivial oscillations in the trans-IR regime while preserving monotonicity. We find evidence that such oscillations appear to drive the trans-IR flow into nontrivial fixed points. We conclude by briefly discussing how our work fits into both the broader program of holographic RG flow and quantum information approaches to probing the black hole interior. 

We study the black hole information problem within a semiclassicallygravitating AdS _d d black hole coupled to and in equilibrium with a d d -dimensionalthermal conformal bath. We deform the bath state by a relevant scalardeformation, triggering a holographic RG flow whose "trans-IR"region deforms from a Schwarzschild geometry to a Kasner universe. Thesetup manifests two independent scales which control both the extent ofcoarse-graining and the entanglement dynamics when counting Hawkingdegrees of freedom in the bath. In tuning either, we find nontrivialchanges to the Page time and Page curve. We consequently view the Pagecurve as a probe of the holographic RG flow, with a higher Page timemanifesting as a result of increased coarse-graining of the bath degreesof freedom. 

A bstract We investigate two sparse Sachdev-Ye-Kitaev (SYK) systems coupled by a bilinear term as a holographic quantum mechanical description of an eternal traversable wormhole in the low temperature limit. Each SYK system consists of N Majorana fermions coupled by random q -body interactions. The degree of sparseness is captured by a regular hypergraph in such a way that the Hamiltonian contains exactly k N independent terms. We improve on the theoretical understanding of the sparseness property by using known measures of hypergraph expansion. We show that the sparse version of the two coupled SYK model is gapped with a ground state close to a thermofield double state. Using Krylov subspace and parallelization techniques, we simulate the system for q = 4 and q = 8. The sparsity of the model allows us to explore larger values of N than the ones existing in the literature for the all-to-all SYK. We analyze in detail the two-point functions and the transmission amplitude of signals between the two systems. We identify a range of parameters where revivals obey the scaling predicted by holography and signals can be interpreted as traversing the wormhole.