Quantum and Gravitational Theory Group

January 18, 2024

January 25, 2024

February 1, 2024

Title: The Virasoro Minimal String

Abstract: I will introduce a critical string theory in two dimensions and explain that this theory, viewed as two-dimensional quantum gravity on the worldsheet, admits an equivalent holographic description in terms of a double-scaled matrix integral. The worldsheet theory consists of Liouville CFT coupled to timelike Liouville CFT. The dual matrix integral has as its leading density of eigenvalues the universal Cardy density of primary states in a two-dimensional CFT of central charge c, which motivates the name of the theory. This duality holds for any value of the continuous parameter c and reduces to the well-known JT gravity/matrix integral duality in the large central charge limit, thus providing a precise stringy realization of JT gravity. Based on work with Lorenz Eberhardt, Beatrix Mühlmann and Victor Rodriguez.

February 8, 2024

Title: Geometric Suprises in the Python's Lunch

Abstract: I will motivate and introduce the Python’s Lunch Conjecture, which, according to Brown et al. controls the complexity of bulk reconstruction in the presence of a bulge surface, which is a non-minimal extremal surface between two locally minimal surfaces homologous to a given boundary region. We study the geometry of bulges in a variety of classical spacetimes, and discover a number of surprising features that distinguish them from more familiar extremal surfaces such as Ryu-Takayanagi surfaces: they spontaneously break spatial isometries, both continuous and discrete; they are sensitive to the choice of boundary infrared regulator; they can self-intersect; they probe entanglement shadows and orbifold singularities; and they probe the compact space in AdSp×Sq. These features imply, according to the python’s lunch conjecture, novel qualitative differences between complexity and entanglement in the holographic context. We also find, surprisingly, that extended black brane interiors have a non-extensive complexity; similarly, for multi-boundary wormhole states, the complexity plateaus after a certain number of boundaries have been included.

February 15, 2024

Title: Pythons

Abstract:  I will continue the discussion on Python’s lunches from Connor Wolfe’s talk. In particular, I will discuss the dependence of complexity on the IR regulator and the saturation of complexity in the case of multi-boundary wormholes. If time permits, I will also discuss some work towards a covariant version of the Python’s lunch.

February 22, 2024

February 29, 2024

Title: Tensor network and Hartle-Hawking state in 3d gravity
Abstract: I will explain the triangulation for the path-integral of Liouville CFT on any 2d surfaces, by proposing a boundary condition for this CFT that allows small holes to close. This will produce an exact analytical tensor network that admits an interpretation of a state-sum of a 3D topological theory constructed with quantum 6j symbols of U_q(Sl(2,R)) with non-trivial boundary conditions, and reduces to Einstein-Hilbert gravity evaluated on hyperbolic spaces in the large central charge limit. The triangulation coincides with producing a network of geodesics in the AdS bulk, which can be changed making use of the pentagon identity and orthogonality condition satisfied by the 6j symbols, and arranged into a precise holographic tensor network. If time permits, I will also describe an identification for the Hartle-Hawking state of BTZ black holes as Liouville ZZ boundary states.

March 7, 2024

Abstract: Any pure state that is reachable from a product state under a finite-depth unitary circuit is trivial in terms of its long-range order. However, mixed states can lose or gain long-range order under finite-depth quantum channels. The question of whether a mixed state possesses long-range order has a definite operational meaning. For example, in the toric code subjected to errors, logical information is retrievable if the error rate is below the error correction threshold. Nevertheless, the metrics proposed to diagnose mixed-state order involve manipulations of multiple copies of the mixed-state density matrix and lack a clear physical interpretation. 

March 14, 2024

Title:  Size Winding Mechanism beyond Maximum Chaos
Abstract: The concept of information scrambling elucidates the dispersion of local information in quantum many-body systems, offering insights into various physical phenomena such as wormhole teleportation. This phenomenon has spurred extensive theoretical and experimental investigations. Among these, the size-winding mechanism emerges as a valuable diagnostic tool for optimizing signal detection. We establish a computational framework for determining the winding size distribution in large-N quantum systems with all-to-all interactions, utilizing the scramblon effective theory. We obtain the winding size distribution for the large-q SYK model across the entire time domain. Notably, we unveil that the manifestation of size winding results from a universal phase factor in the scramblon propagator, highlighting the significance of the Lyapunov exponent. These findings contribute to a sharp and precise connection between operator dynamics and the phenomenon of wormhole teleportation.

March 21, 2024

March 28, 2024

April 4, 2024

Title: Cryptographic Censorship
Abstract: I will talk about my recent work (https://arxiv.org/abs/2402.03425) with Netta Engelhardt, Åsmund Folkestad, Adam Levine, and Evita Verheijden. We formulate and take two large strides towards proving a quantum version of the weak cosmic censorship conjecture. We first prove "Cryptographic Censorship": a theorem showing that when the time evolution operator of a holographic CFT is approximately pseudorandom (or Haar random) on some code subspace, then there must be an event horizon in the corresponding bulk dual. This result provides a general condition that guarantees (in finite time) event horizon formation, with minimal assumptions about the global spacetime structure. Our theorem relies on an extension of a recent quantum learning no-go theorem and is proved using new techniques of pseudorandom measure concentration. To apply this result to cosmic censorship, we separate singularities into classical, semi-Planckian, and Planckian types. We illustrate that classical and semi-Planckian singularities are compatible with approximately pseudorandom CFT time evolution; thus, if such singularities are indeed approximately pseudorandom, by Cryptographic Censorship, they cannot exist in the absence of event horizons. This result provides a sufficient condition guaranteeing that seminal holographic results on quantum chaos and thermalization, whose general applicability relies on typicality of horizons, will not be invalidated by the formation of naked singularities in AdS/CFT.

April 11, 2024

April 18, 2024

Title: New Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity
Abstract: We consider four-dimensional Euclidean gravity in a finite cavity. We point out that there exists a one-parameter family of boundary conditions, parameterized by a real constant, where a suitably Weyl-rescaled boundary metric is fixed, and all give a well-posed elliptic system, as opposed to the Dirichlet boundary condition. Focussing on static Euclidean solutions, we derive a thermodynamic first law. Restricting to a spherical spatial boundary, the infillings are flat space or the Schwarzschild solution, and have similar thermodynamics to the Dirichlet case. We study the stability behavior of several geometries under these boundary conditions in both Euclidean and Lorentzian signatures and find two puzzles.