Berry curvature of BPS states is random-matrix-like for supersymmetric black hole microstates but non-random and often zero for horizonless geometries, offering a chaos diagnostic in degenerate sectors.
Complex matrix model and fermion phase space for bubbling AdS geometries
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abstract
We study a relation between droplet configurations in the bubbling AdS geometries and a complex matrix model that describes the dynamics of a class of chiral primary operators in dual N=4 super Yang Mills (SYM). We show rigorously that a singlet holomorphic sector of the complex matrix model is equivalent to a holomorphic part of two-dimensional free fermions, and establish an exact correspondence between the singlet holomorphic sector of the complex matrix model and one-dimensional free fermions. Based on this correspondence, we find a relation of the singlet holomorphic operators of the complex matrix model to the Wigner phase space distribution. By using this relation and the AdS/CFT duality, we give a further evidence that the droplets in the bubbling AdS geometries are identified with those in the phase space of the one-dimensional fermions. We also show that the above correspondence actually maps the operators of N=4 SYM corresponding to the (dual) giant gravitons to the droplet configurations proposed in the literature.
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Near a cusp in the LLM droplet, the geometry acquires a universal ISO(1,3)×SO(5) symmetric form with a naked singularity that traps both massless and massive particles, admitting analytic massless trajectories and hinting at integrability.
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Chaos of Berry curvature for BPS microstates
Berry curvature of BPS states is random-matrix-like for supersymmetric black hole microstates but non-random and often zero for horizonless geometries, offering a chaos diagnostic in degenerate sectors.
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Critical Lin-Lunin-Maldacena geometries
Near a cusp in the LLM droplet, the geometry acquires a universal ISO(1,3)×SO(5) symmetric form with a naked singularity that traps both massless and massive particles, admitting analytic massless trajectories and hinting at integrability.