Talks

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...

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.