Quantum Gravity

A number of recent arguments have suggested that baby universes in quantum gravity have a one-dimensional Hilbert space. I will provide a new argument, based on work with E. Gesteau, in favor of this conclusion. The argument makes use of a standard asymptotically AdS spacetime dual to a thermal state below the Hawking-Page transition. In particular, there is a low-energy, low-complexity causal wedge operator whose expectation value in the dual CFT is only consistent with a one-dimensional Hilbert space for baby universes.

The `quantum gravity in the lab' paradigm suggests that quantum computers might shed light on quantum gravity by simulating the CFT side of the AdS/CFT correspondence and mapping the results to the AdS side. This relies on the assumption that the duality map (the `dictionary') is efficient to compute. In this talk, I will argue that the complexity of the AdS/CFT dictionary is surprisingly subtle: there might be cases in which one can efficiently apply operators to the CFT state (a task we call 'operator reconstruction') without being able to extract basic properties of the dual bulk state such as its geometry (which we call 'geometry reconstruction'), and vice versa. In order to reason about the complexity of geometry reconstruction we construct examples of holographic pseudoentanglement: that is, pairs of ensembles of states that obey the Ryu-Takayanagi formula for different geometries but which are nevertheless computationally indistinguishable. This result should be compared with existing evidence that operator reconstruction is generically easy in AdS/CFT. A useful analogy for the difference between these two tasks is quantum fully homomorphic encryption (FHE): this encrypts quantum states in such a way that no efficient adversary can learn properties of the state, but operators can be applied efficiently to the encrypted state. I will show that quantum FHE can separate the complexity of geometry reconstruction vs operator reconstruction, which raises the question whether FHE could be a useful lens through which to view AdS/CFT.

The gravitational path integral remains one of the most elusive constructs in quantum gravity, particularly in regimes dominated by topological fluctuations. In this talk, I will present recent progress in Jackiw–Teitelboim (JT) gravity, where the sum over geometries can be made precise. We demonstrate that in a low-temperature regime where semiclassical approximations fail, the all-genus thermal partition function of JT gravity admits a resummation into an effective description on a single geometry with a nonlocal deformation. This construction gives formal and geometric realization to long-standing ideas from the 1980s on wormhole-induced nonlocality, linking them to ensemble interpretations and topological expansions. The resulting theory, defined on the disk with conical defect operators, captures the complete topological expansion through an emergent nonlocal interaction, providing a precise geometric window into strongly quantum gravitational dynamics.

A diffeomorphism-invariant definition of physical subsystems is crucial for understanding local quantum information in gravity. Recent toy models have made progress by adding observers with clocks and imposing boost invariance, thereby enabling a rigorous von Neumann algebraic definition of generalized entropy. But they depend on auxiliary degrees of freedom and leave infinitely many diffeomorphisms unaddressed. It is natural to ask what happens when one tries to surmount these limitations. I’ll show that including null translations lets us prove a version of the generalized second law beyond the semiclassical regime, with potential direct implications for black hole information. Then I’ll outline how the area degrees of freedom on a null surface define a quantum null time coordinate, and show how to use it to construct dressed operators invariant under all null diffeomorphisms (work in progress with Laurent Freidel.)

The SYK model has attracted significant interest for its maximal chaos, connections to two-dimensional holography, and relevance to strange metals. Two signatures of chaos in this model are out-of-time-ordered correlators (OTOCs) and Krylov complexity, both exhibiting early-time exponential behaviours characterized by the Lyapunov and Krylov exponents, respectively. In this talk, I explore these quantities in a class of relevant deformations of the SYK model, including flows which interpolate between two regions of near-maximal chaos and flows that lead to a nearly-integrable behaviour at low temperatures. I present both analytic and numerical results showing that the Krylov exponent consistently upper-bounds the Lyapunov exponent. Notably, while the Lyapunov exponent varies non-monotonically with temperature, the Krylov exponent remains smooth and monotonic, showing no clear signatures across chaotic transitions. This challenges the effectiveness of Krylov complexity as a diagnostic of chaos in quantum mechanical systems. I will also comment on the potential relevance of SYK flows for de Sitter holography and on connections to other recent works.

The holographic calculation of entanglement entropy implies that space coordinate in gravity may emerge from quantum entanglement. The next key question will be to understand how time coordinate may emerge from quantum information. After we review recent developments of pseudo entropy, which is a generalization of entanglement entropy, and its holographic calculation, we will point out that this quantity looks like a useful starting point to understand the emergence of time, by studying explicit examples of time-like entanglement entropy, traversable wormhole and dS/CFT. In the final short time, we would also like to briefly discuss how much the AdS/CFT is efficient as a quantum computer, where the notion of pseudo entanglement in the context of pseudo random states, plays an important role.

One of the fundamental problems in quantum gravity is to describe the experience of a gravitating observer in generic spacetimes. In this talk, I will describe a framework within which we can analyze non-perturbative physics relative to an observer using the gravitational path integral. We apply our proposal to an observer that lives in a closed universe and one that falls behind a black hole horizon. We find that the Hilbert space that describes the experience of the observer is much larger than the Hilbert space in the absence of an observer. In the case of closed universes, the Hilbert space is not one-dimensional, as calculations in the absence of the observer suggest. Rather, its dimension scales exponentially in 1/G_N. Similarly, from an observer's perspective, the dimension of the Hilbert space in a two-sided black hole is increased and this drastically changes what an observer sees when falling past the horizon of a black hole at late times.

In this talk I will report on recent developments concerning quantization of field theories on manifolds with boundary. In perturbative AQFT this can be realized using a version of BV-BFV formalism, following the program outlined by Mnev, Cattaneo and Reshetikin. I will also argue that in pAQFT one always implicitly introduces boundaries and that there are good conceptual reasons to do so. This is joint work with Michele Schiavina.

I will describe various constructions of cosmological spacetimes with big bangs using the tools of holography. I will point out features that appear to be common to holographic models of cosmology and discuss general questions that these models might be used to understand.