Talks

Outline of Topics:

Minimal Surfaces in Diblock Copolymers: the P,G, and D triply periodic minimal surfaces.
Smectic Liquid Crystals: the simplest crystals and they are built from surfaces.
Using minimal surfaces to knit: geometric scaffolds in materials science.

I will describe recent work which defines a class of multi-party measures of entanglement which are characterized by tensorial contractions of copies of a density matrix with respect to an arbitrary finite group symmetry.

For AdS3/CFT2 they can be determined by both boundary replica trick calculations of twist operators and by bulk quotients of Euclidean AdS3 by Kleinian groups. The technology developed allows for the determination of all such measures which can preserve bulk replica symmetry.

I will provide several explicit examples including a complete classification of measures with genus zero and one replica surfaces.

First Talk (90 minutes) I would like to give a brief introduction of spacelike hypersurfaces and maximal hypersurfaces in Minkowski space. Then I would like to introduce maximal surfaces with singularities in Minkowsiki 3-space and give examples.

I will review recent work on using geometric phases for describing the entanglement properties of spacetimes, in particular black holes. In particular, similarities and differences between simple quantum mechanical systems and quantum gravity will be presented and discussed.

We match instanton contributions between (2,4k) minimal superstring theory with type 0B GSO projection and its dual unitary matrix integral. The main technical insight is to use string field theory to analyze and cure the divergences in the cylinder diagram with both boundaries on a ZZ brane. This procedure gives a finite normalization constant for the non-perturbative effects in minimal superstring theory. Based on arXiv:2406.16867

It was conjectured that a holographic CFT deformed by the TTbar operator is dual to a bulk with a finite radial cutoff. I will describe a sequence of deformations that appear to push the cutoff surface into the black hole interior. The finite boundary is always at a constant radial surface, which means it changes signature when in the interior. I will provide a bulk path integral whose saddles describe these bulk spacetimes with finite spacelike cutoff surfaces. These results are restricted to 3d and JT gravity. This is based on work with Shadi Ali Ahmad and Simon Lin.

In quantum many-body systems, ‘measurement-induced phase transitions’ (MIPT), have led to a new paradigm for dynamical phase transitions in recent years. I will first discuss a model of continuously monitored or weakly measured arrays of Josephson junctions (JJAs) with feedback. Using a combination of a variational self-consistent harmonic approximation and analysis in the semiclassical limit, strong dissipation limit, and weak coupling perturbative renormalization group, I will show that the model undergoes reentrant superconductor-insulator MIPTs in its long-time non-equilibrium steady state as a function of measurement strength and feedback strength. I will contrast the phase diagram of monitored JJA with the well-studied case of dissipative JJA. In the second part of the talk, starting from a similar model of a continuously monitored chain of coupled anharmonic oscillators with feedback, I will show that the quantum dynamics maps to a stochastic Langevin dynamics with noise strengt...

We consider a class of exactly solvable Hamiltonian deformations of Conformal Fields Theories (CFTs) in arbitrary dimensions. The deformed Hamiltonians involve generators which form a SU(1,1) subalgebra. The Floquet and quench dynamics can be computed exactly. The CFTs exhibit distinct heating and non-heating phases at late times characterized by exponential and oscillatory correlators as functions of time. When the dynamics starts from a homogenous state, the energy density is shown to localize spatially in the heating phase. The set-ups considered will involve step pulses of different Hamiltonians, but can be generalized to smooth drives. In low dimensions we verify our results with lattice numerics.

Abstract:  In relativity, the geometry of the light cones determines the causal structure of spacetime. Under the influence of gravity, the light cones bend and curve. A previously expanding light cone can fall back into itself. In this way, the causal structure becomes a dynamical aspect of spacetime. How do we understand this link between gravity, geometry and causality at the quantum level? Is there a quantum light cone geometry? In my talk, I will argue that the answer to this problem is crucial for making progress in quantum gravity. It is, in fact, a problem that is shared among different approaches, from holography, to celestial amplitudes and loop quantum gravity. In my presentation, I report on three new results on this frontier. First, I provide a non-perturbative characterization of impulsive gravitational null initial data for tetradic gravity on a light cone. Second, the description is taken to the quantum level. Third, an immediate physical implication is found: in the model, the Planck luminosity separates the eigenvalues of the radiated power. Below the Planck power, the spectrum of the radiated power is discrete. Above the Planck power, the spectrum is continuous and the resulting physical states contain caustics that can spoil the semi-classical limit.  The talk is based on arXiv:2402.12578, arXiv:2401.17491, arXiv:2104.05803.

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...