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A<sc>bstract</sc> The D0-brane/Banks-Fischler-Shenker-Susskind matrix theory is a strongly coupled quantum system with an interesting gravity dual. We develop a scheme to derive bootstrap bounds on simple correlators in the matrix theory at infiniteNat zero energy by imposing the supercharge equations of motion. By exploiting SO(9) symmetry, we are able to consider single-trace operators involving words of length up to 9 using very modest computational resources. We interpret our initial results as strong evidence that the bootstrap method can efficiently access physics in the strongly coupled, infiniteNregime. 

Black holes are chaotic quantum systems that are expected to exhibit random matrix statistics in their finite energy spectrum. Lin, Maldacena, Rozenberg and Shan (LMRS) have proposed a related characterization of chaos for the ground states of BPS black holes with finite area horizons. On a separate front, the “fuzzball program” has uncovered large families of horizon-free geometries that account for the entropy of holographic BPS systems, but only in situations with sufficient supersymmetry to exclude finite area horizons. The highly structured, non-random nature of these solutions seems in tension with strong chaos. We verify this intuition by performing analytic and numerical calculations of the LMRS diagnostic in the corresponding boundary quantum system. In particular we examine the 1/2 and 1/4-BPS sectors of\mathcal{N}=4 $𝒩=4$SYM, and the two charge sector of the D1-D5 CFT. We find evidence that these systems are only weakly chaotic, with a Thouless time determining the onset of chaos that grows as a power ofN $N$. In contrast, finite horizon area BPS black holes should be strongly chaotic, with a Thouless time of order one. In this case, finite energy chaotic states become BPS asN $N$is decreased through the recently discovered “fortuity” mechanism. Hence they can plausibly retain their strongly chaotic character. 

A<sc>bstract</sc> A feature the$$ \mathcal{N} $$ $N$= 2 supersymmetric Sachdev-Ye-Kitaev (SYK) model shares with extremal black holes is an exponentially large number of ground states that preserve supersymmetry. In fact, the dimension of the ground state subsector is a finite fraction of the total dimension of the SYK Hilbert space. This fraction has a remarkably simple bulk interpretation as the probability that the zero-temperature wormhole — a supersymmetric Einstein-Rosen bridge — has vanishing length. Using chord techniques, we compute the zero-temperature Hartle-Hawking wavefunction; the results reproduce the ground state count obtained from boundary index computations, including non-perturbative corrections. Along the way, we improve the construction [1] of the super-chord Hilbert space and show that the transfer matrix of the empty wormhole enjoys an enhanced$$ \mathcal{N} $$ $N$= 4 supersymmetry. We also obtain expressions for various two point functions at zero temperature. Finally, we find the expressions for the supercharges acting on more general wormholes with matter and present the superchord algebra. 

Post-Wilsonian physics views theories not as isolated points but elements of bigger universality classes, with effective theories emerging in the infrared. This paper makes initial attempts to apply this viewpoint to homogeneous geometries on group manifolds, and complexity geometry in particular. We observe that many homogeneous metrics on low-dimensional Lie groups have markedly different short-distance properties, but nearly identical distance functions at longer distances. Using Nielsen's framework of complexity geometry, we argue for the existence of a large universality class of definitions of quantum complexity, each linearly related to the other, a much finer-grained equivalence than typically considered in complexity theory. We conjecture that at larger complexities, a new effective metric emerges that describes a broad class of complexity geometries, insensitive to various choices of 'ultraviolet' penalty factors. Finally we lay out a broader mathematical program of classifying the effective geometries of right-invariant group manifolds.