Microscopic Origin of the Entropy of Astrophysical Black Holes.

We construct an infinite family of microstates for black holes in Minkowski spacetime which have effective semiclassical descriptions in terms of collapsing dust shells in the black hole interior. Quantum mechanical wormholes cause these states to have exponentially small, but universal, overlaps. We show that these overlaps imply that the microstates span a Hilbert space of log dimension equal to the event horizon area divided by four times the Newton constant, explaining the statistical origin of the Bekenstein-Hawking entropy.

Generalized Symmetries for Generalized Gravitons.

We construct generalized symmetries for linearized Einstein gravity in arbitrary dimensions. First-principle considerations in quantum field theory force generalized symmetries to appear in dual pairs. Verifying this prediction helps us find the full set of nontrivial conserved charges-associated, in equal parts, with 2-form and (D-2)-form currents. Their total number is D(D+1). We compute the quantum commutators of pairs of dual charges, showing that they are nonvanishing for regions whose boundaries are nontrivially linked with each other and zero otherwise, as expected on general grounds. We also consider general linearized higher-curvature gravities. These propagate, in addition to the usual graviton, a spin-0 mode as well as a massive ghostlike spin-2 mode. When the latter is absent, the theory is unitary and the dual-pairs principle is respected. In particular, we find that the number and types of charges remain the same as for Einstein gravity, and that they correspond to continuous generalizations of the Einsteinian ones.

Quantum Computation as Gravity.

We formulate Nielsen's geometric approach to circuit complexity in the context of two-dimensional conformal field theories, where series of conformal transformations are interpreted as "unitary circuits" built from energy-momentum tensor gates. We show that the complexity functional in this setup can be written as the Polyakov action of two-dimensional gravity or, equivalently, as the geometric action on the coadjoint orbits of the Virasoro group. This way, we argue that gravity sets the rules for optimal quantum computation in conformal field theories.

Random Free Fermions: An Analytical Example of Eigenstate Thermalization.

Having analytical instances of the eigenstate thermalization hypothesis (ETH) is of obvious interest, both for fundamental and applied reasons. This is generally a hard task, due to the belief that nonlinear interactions are basic ingredients of the thermalization mechanism. In this article we prove that random Gaussian-free fermions satisfy ETH in the multiparticle sector, by analytically computing the correlations and entanglement entropies of the theory. With the explicit construction at hand, we finally comment on the differences between fully random Hamiltonians and random Gaussian systems, providing a physically motivated notion of randomness of the microscopic quantum state.