Conference

Our search for a quantum theory of gravity is aided by a unique and perplexing feature of the classical theory: General Relativity “knows” about its own quantum states (the entropy of a black hole), and about those of all matter (via the Quantum Focusing Conjecture). The results we are able to extract from classical gravity are inherently non-perturbative and increasingly sophisticated. Recent breakthroughs include a derivation of the entropy of Hawking radiation, a computation of the exact integer number of states of some black holes, a proof of the QFC, and the construction of gravitational holograms in general spacetimes. The nature of the oracle, and its full power, remain unknown.

The Ryu-Takayanagi formula implies that the entropy, a non-linear function of the state, is an observable in the semiclassical limit. This is a general phenomenon in a class of quantum error-correcting codes (QECC), but few specific area operators in the boundary CFT. In this work, I define a specific code in a holographic 2d CFT that includes all thermofield double states with arbitrary amounts of time evolution, but no bulk local degrees of freedom. While the naive area operator vanishes, it is possible to write down an area operator for appropriately classical states; the answer matches with previous results obtained from bulk considerations. Interestingly, this area operator involves an explicit coarse-graining. This suggests a construction for a non-isometric holographic map for these states.

The entanglement entropy for regions in a BMS field theory living at null infinity has been proposed to be holographically dual to certain ‘swing surfaces’ in flat space. We lift this construction to AdS/CFT and revisit both bulk and boundary aspects of this proposal.

In quantum gravity, the gravitational path integral involves a sum over topologies, representing the joining and splitting of multiple universes. To account for topology change, one is led to allow the creation and annihilation of both closed and open universes in a framework often called third quantization or universe field theory. We argue that since topology change in gravity is a rare event, its contribution to late-time physics should be universally governed by a Poisson distribution. In the Fock space of closed baby universes, this Poisson distribution corresponds to the statistics of the number operator in a coherent state, whereas allowing for the creation of asymptotic open universes calls for a non-commutative generalization of a Poisson process. We propose such an operator algebraic framework, called Poissonization, which takes as input the observable algebra and a (unnormalized) state of a quantum system and outputs a von Neumann algebra represented on its symmetric Fock space. Physically, our construction is a generalization of the coherent state vacua of bipartite quantum systems.

We construct algebras of diff-invariant observables in a global de Sitter universe with two observers and a free scalar QFT in two dimensions. In the limit when the observers have infinite mass and are localized along geodesics at the North and South poles, it was shown in previous work (CLPW) that their algebras are mutually commuting type II_1 factors. Away from this limit, we show that the algebras fail to commute and that they are type I non-factors. Physically, this is because the observers' trajectories are uncertain and state-dependent, and they may come into causal contact. We compute out-of-time-ordered correlators along an observer's worldline, and observe a Lyapunov exponent given by 4πβ_dS, as a result of observer recoil and de Sitter expansion. This should be contrasted with results from AdS gravity, and exceeds the chaos bound associated with the de Sitter temperature by a factor of two. We also discuss how the cosmological horizon emerges in the large mass limit and comment on implications for de Sitter holography.

Ordered structures that tile the plane in an aperiodic fashion - thus lacking translational symmetry - have long been considered in the mathematical literature. A general method for the construction of quasicrystals is known as *cut-and-project* ($\mathsf{CNP}$ for short), where an irrational slice "cuts" a higher-dimensional space endowed with a lattice and suitably chosen lattice points are further "projected down" onto the subspace to form the vertices of the quasicrystal. However, most of the known examples of $\mathsf{CNP}$ quasi-tilings are Euclidean. In this talk, after presenting the main ingredients of the Euclidean prescription, we will extend it to Lorentzian spacetimes and develop Lorentzian $\mathsf{CNP}$. This will allow us to discuss the first ever examples of Lorentzian quasicrystals, one in $(1+1)$- and another in $(1+3)$-dimensional spacetime. Finally, we will argue why the latter construction might be relevant for *our Lorentzian spacetime*. In particular, we shall appreciate how the picture of a quasi-crystalline spacetime could provide a potentially new string-compactification scheme that can naturally accommodate for the hierarchy problem and the smallness of our cosmological constant. Lastly, we will comment on its relevance to quantum geometry and quantum gravity; first, as a conformal Lorentzian structure of no intrinsic scale, and second through the connection of quasicrystals to quantum error-correcting codes.

Modern quantum simulations methods often use a fictitious imaginary time introduced by Feynman to exactly transform static quantum problems to dynamic imaginary time classical ones [1]. In addition to imaginary time simulation methods such as centroid molecular dynamics and path integral Monte Carlo, one can apply this quantum-classical isomorphism to self-consistent field theory (SCFT). An advantage of the field-theoretic perspective is that it can be exactly transformed into quantum density functional theory (DFT), meaning that the theorems of DFT (Hohenberg-Kohn and Mermin theorems) prove an equivalence between classical imaginary time SCFT dynamics and static quantum results [2]. Since imaginary time is assigned the same properties as regular time, one can replace the imaginary time in the SCFT equations with real time (a Wick rotation), which gives the equations of time-dependent DFT. The time-dependent DFT theorem (Runge-Gross theorem) then proves that one obtains all results of standard quantum mechanics from this imaginary time classical starting point. These results make it very tempting to consider treating imaginary time as an element of reality. This quantum reconstruction from imaginary time will be discussed, including a speculative look at treating imaginary time in the context of special relativity, with a preliminary comparison to the deformed special relativity of Magueijo and Smolin. [1] D. M. Ceperely, Reviews of Modern Physics 67, 279 (1995) [2] R. B. Thompson, Journal of Chemical Physics 150, 204109 (2019) [3] J. Magueijo and L. Smolin, Physical Review D 67, 044017 (2003)

Based on a previously published model of a quantum gravity path integral, expressed in spectral-geometric variables (Phys. Rev. Lett. 131, 211501), co-authored with M. Reitz and A. Kempf, I study the emergence of Lorentzian signature and time dimension from quantum fluctuations, and argue the physical intuition behind it via a known condensed matter phenomenon.