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We have now come to understand that extremal black holes are like ordinary quantum systems with a few degrees of freedom, and no macroscopic degeneracy. The classical black hole entropy receives quantum corrections, from collective modes localized in the near-horizon region, that lowers the density of states. I will describe an alternate perspective on these quantum effects, focusing on the entire spacetime. Specifically, I will argue that the near-extremal black holes support a set of low-lying gapless modes which are responsible for this suppression of the degeneracy at low temperatures.

Analytic continuations of areas of Ryu-Takayanagi surfaces in which the boundary subregion becomes extended along a timelike direction brought a promise of a novel, time-centric probe of the emergence of spacetime. We propose that the bulk carrier of this holographic timelike entanglement entropy are boundary-anchored extremal surfaces probing analytic continuation of holographic spacetimes into complex coordinates. This not only provides a geometric interpretation of all the known cases obtained by direct analytic continuation of closed form expressions of holographic entanglement entropy of a strip subregion, but crucially also opens a window to study holographic timelike entanglement entropy in full generality. To better understand what the prescription for holographic timelike entanglement entropy entails we study complex extremal surfaces anchored on a timelike strip on the boundary of anti-de Sitter black hole spacetimes. Our investigation reveals the existence of multiple comple...

We formulate the non relativistic quantum description of a collection of particles, in specified but arbitrary representations of the gauge group, interacting via a Chern Simons coupled gauge field. We argue that the quantum systems so constructed enjoy invariance under level rank duality.

Recently, S. Murthy has proposed a convergent expansion of free partition functions and superconformal indices of finite-N purely adjoint gauge theories based on a Fredholm determinant expansion. This expansion has been dubbed the giant graviton expansion and takes the form of an infinite series of corrections to the N=∞ result, with the m-th correction being of order exp(−mN). We show that this expansion can be reproduced using eigenvalue instantons in unitary matrix integrals. This perspective allows us to get the giant graviton expansion without the intermediate step of the Hubbard Stratonovich transformation.

I will describe extremal surfaces in de Sitter space anchored at the future boundary I+. Since such surfaces do not return, they require extra data in the past. In entirely Lorentzian dS, this leads to future-past timelike surfaces stretching between I+/I-, with pure imaginary area (relative to spacelike surfaces in AdS). With a no-boundary type boundary condition, the top half of these joins with a spacelike part on the hemisphere giving a complex-valued area. These can be thought of as certain analytic continuations from AdS while also amounting to space-time rotations. The areas are best interpreted as pseudo-entropy or time-entanglement (entanglement-like structures with timelike separations). I will also briefly discuss multiple subregions, entropy relations, the pseudo-entanglement wedge, a heuristic Lewkowycz-Maldacena formulation, as well as aspects in toy models in quantum mechanics, involving the time evolution operator, reduced transition amplitudes, and future-past entangle...

We consider linear superpositions of single particle excitations in a scalar field theory on AdS3 and evaluate their contribution to the bulk entanglement entropy across the Ryu-Takayanagi surface. We compare the entanglement entropy of these excitations obtained using the Faulkner-Lewkowycz-Maldacena formula to the entanglement entropy of linear superposition of global descendants of a conformal primary in a large c CFT obtained using the replica trick. We show that the closed from expressions for the entanglement entropy in the small interval expansion both in gravity and the CFT precisely agree. The agreement serves as a non-trivial check of the FLM formula for the quantum corrections to holographic entropy which also involves a contribution from the back reacted minimal area. Our checks includes an example in which the state is time dependent and spatially in-homogenous as well another example involving a coherent state with a Bañados geometry as its holographic dual.

The emergent geometry from large N matrix models is shown to be naturally granular, with a short distance cut-off proportional to 1/N. This is explicitly demonstrated for matrix quantum mechanics which is exactly mapped to a lattice boson with lattice spacing  1/N. In case of the double scaled c=1 matrix model, even though N is infinite, the exact boson theory has an effective short distance cutoff given by a scaled quantity proportional to the string coupling. This explains the finite entanglement entropy and finite S matrix elements of the 2D string theory in contrast with collective field theory where these quantities are divergent. We  also briefly discuss a lattice boson representation of time-dependent unitary matrix models.

In recent years, it has been realized that algebraic techniques can be used to compute formal entropy differences for semiclassical black holes in quantum gravity, and that these entropy differences are consistent with the Bekenstein-Hawking formula. I will explain how to remove the word "formal" from the previous sentence, by showing that the algebraic entropy differences have an interpretation in terms of microstate counting that is consistent with our usual ideas about statistical mechanics. Based on 2404.16098 with Akers.

What is the bulk Hilbert space of quantum gravity? In this paper, we resolve this problem in 2d JT gravity, both with and without matter, providing the first example of an explicit definition of a non-perturbative Hilbert space specified in terms of metric variables. The states are wavefunctions of the length and matter state, but with a non-trivial and highly degenerate inner product. We explicitly identify the null states, and discuss their importance for defining operators non-perturbatively. To highlight the power of the formalism we developed, we study the non-perturbative effects for two bulk linear operators that may serve as proxies for the experience of an observer falling into a two-sided black hole: one captures the length of an Einstein-Rosen bridge and the other captures the center-of-mass collision energy between two particles falling from opposite sides. We track the behavior of these operators up to times of order eSBH, at which point the wavefunction spreads to the com...

We will introduce (standard) future operator algebras. We show that standard future algebras transform covariantly under the action of an emergent (universal cover of) PSL(2,R). In the case of generalized free fields with spectral densities corresponding to AdS_2 and higher dimensional eternal black holes, this symmetry corresponds to, respectively, the bulk AdS_2 and the conformal symmetry on the horizon.

Humanity faces real and present problems. Our resources to address these problems are limited. It’s easy to think, then, that we should devote ourselves to our most promising solutions.

It’s easy, but it’s wrong.

The great paradox of scientific research is that pure exploration – research into deep questions motivated by pure curiosity, without concern for applications – is ultimately what transforms our lives in tangible, practical ways.

In this talk, I will speak not just as a physicist interested in puzzles of quantum entanglement and five-dimensional black holes, but as the director of an institute devoted to fundamental research. I make the case for blue-sky research, and for optimism about our shared future.