Monday, 12 August 2024

The phase diagram of extremal black holes in supergravity is surprisingly rich. In some regimes, quantum effects are so strong that they dominate. On the supersymmetric locus, there is a large ground state degeneracy, protected by a gap. Throughout, there is an intricate classical interplay between charge and rotation that gives rise to instability via various mechanisms, including superradiance and superconductivity. The talk highlights examples from black holes in AdS(3) and AdS(5).

Tuesday, 13 August 2024

Everything Everywhere All at Once: Holographic Entropy Inequalities, Entanglement Wedge Nesting, Topology of Error Correction, Black Holes, Cubohemioctahedron (and maybe the Toric Code)

Recently, a new interpretation of gravitational spacetime in terms of quantum entanglement has been developed. The idea of holography in string theory provides a simple geometric computation of entanglement entropy. This generalizes the well-known Bekenstein-Hawking formula of black hole entropy and strongly suggests that a gravitational spacetime consists of many qubits with quantum entanglement. Also a new progress on black hole information problem has been made recently by applying this idea. A new insight on holography for de Sitter spaces have also been obtained from quantum information viewpoints. I will explain these developments in this lecture.

Wednesday, 14 August 2024

AdS/CFT correspondence has played crucial roles to understand difficult problems in quantum gravity in terms of quantum field theories. When a conformal field theory (CFT) is defined on a manifold with boundaries, we can generalize the standard AdS/CFT by introducing so called end-of-the-world branes. This extended holographic duality, called AdS/BCFT, captures, for examples, the essential feature of quantum gravity such as the black hole information problem. In this lecture, I would like to explain how this holographic duality works and discuss recent developments.

This talk explores the connections between quantum error correction (QEC) and the renormalization group (RG) in three parts:

First, we review the operator algebraic formulation of QEC.

Second, we apply this formalism to demonstrate that real-space RG flow prepares approximate local QEC codes in the infrared.

Third, we make this connection explicit by showing that the exact RG flow of density matrices is described by a Lindblad master equation.

Friday, 16 August 2024

Traditionally, measurements have been synonymous with extracting information from physical systems. Yet, in quantum systems measurement can actively modify and steer quantum states, acting as a quantum chisel to sculpt new patterns of entanglement. I will describe how this power of measurements can be leveraged to efficiently create the long sought after non-Abelian topological phases. Surprisingly, the particular non-Abelian states created in this way are closely related to Galois' characterization of solvable polynomial equations.

Finally, I will describe our recent collaboration with Quantinuum that utilizes this approach. In particular, I will discuss the Borromean braiding of excitations, a signature unique to non Abelian topological order, and its measurement on the Quantinuum platform.

Pseudo entropy is an interesting quantity with a simple gravity dual, which generalizes entanglement entropy such that it depends on both an initial and a final state. In this talk we start with an introduction of this new quantity explaining its basic properties and its holographic calculations. Next, we will present recent numerical results of this quantity in a free scalar field theory and in a spin system, which imply that pseudo entropy can serve as a new quantum order parameter. Finally, we will discuss an application of pseudo entropy to holography in de Sitter spaces and to entanglement phase transitions.

Monday, 19 August 2024

We will see that Shannon entropy arises naturally from the problem of efficiently representing the outcome of a probabilistic experiment as a string of bits. We will review entropic quantities such as relative entropy, conditional entropy and mutual information, and relate them to notions such as the rate of growth of the number of typical sequences and asymptotic limits on the rate of information transmission across a noisy channel.

Tuesday, 20 August 2024

We will present the basic inequalities concerning the classical entropic quantities introduced in the first lecture. We will then proceed to the quantum analogue of Shannon entropy. We will first briefly review pure and mixed states, and their evolution. We will then present Von Neumann entropy, and other related quantum mechanical entropic quantities, study their properties, and present the basic inequalities.

Wednesday, 21 August 2024

The description of a quantum many-body system lacking quasiparticles is a longstanding challenge at the forefront of physics. A solvable example is provided by the Sachdve-Ye-Kitaev (SYK) model, which has attracted much attention due to its intriguing connections to black holes and intertwined questions on non-Fermi liquid metals, thermalization, and many-body quantum chaos. After a brief review of the phenomenology of Fermi (FL) and non-Fermi (NFL) liquids, I will give a pedagogical introduction to the large-N saddle-point method, spectral and thermodynamics properties, and the computation of the out-of-time-ordered correlation and Lyapunov exponent in the SYK model. I will then discuss a few generalizations/extensions of the SYK model with NFL-FL and other dynamical transitions. I will conclude with a discussion of an experimental realization of the SYK model in condensed matter systems.

We will discuss connections between quantum relative entropy and other distance measures between probability distributions and quantum states. We will discuss the connection to hypothesis testing. If there is time, we will present applications of classical and quantum information theory to problems in combinatorics and computer science.

Friday, 23 August 2024

Motivated by SYK model, there have been a lot of activities to understand quantum dynamics in interacting systems via many-body quantum chaos and describe a variety of quantum phases, e.g., heavy Fermi liquids, marginal and non-Fermi liquid, correlated superconductors, etc., through generalizations of the SYK model. I will first discuss some quantum spin glass models related to the SYK model and the characterization of their dynamics through chaos. I will then discuss some lattice and higher-dimensional generalizations of the SYK model to understand higher-dimensional non-Fermi liquids, such as strange metals and other correlated phases.

Saturday, 24 August 2024

Characterization of quantum many-body phases through entanglement and non-equilibrium dynamics, such as thermalization, has become a major area of research in recent years. I will discuss calculations of subsystem Renyi entropy in SYK and related models in the large-N limit, mainly based on a new path integral method for computing entanglement entropy of interacting fermions. I will then discuss the non-equilibrium dynamics of SYK models within large-N Schwinger-Keldysh field theory and using finite-N numerics, starting from different types of non-equilibrium initial conditions, like after sudden or slow quenches in the Fermi liquid (FL), non-Fermi liquid (NFL) phases and across NFL-FL transition, as well as starting from a generic pure product state.

Monday, 26 August 2024

I will give an overview of notions of entanglement of color degrees of freedom relevant to the holographic correspondence

We define a relational notion of a subsystem in theories of matrix quantum mechanics and show how the corresponding entanglement entropy can be given as a minimisation, exhibiting many similarities to the Ryu-Takayanagi formula. Our construction brings together the physics of entanglement edge modes, noncommutative geometry and quantum internal reference frames, to define a subsystem whose reduced state is (approximately) an incoherent sum of density matrices, corresponding to distinct spatial subregions. We show that in states where geometry emerges from semiclassical matrices, this sum is dominated by the subregion with minimal boundary area. As in the Ryu-Takayanagi formula, it is the computation of the entanglement that determines the subregion. We find that coarse-graining is essential in our microscopic derivation, in order to control the proliferation of highly curved and disconnected non-geometric subregions in the sum.

In this talk I will discuss multi-partite entanglement measures and their computation for holographic theories. I will focus on a particular class of the measures called symmetric measures. If the replica symmetry of the measure is preserved by the bulk solution, then the measure is described by a space with conical singularities whose underlying topology is that of a ball. I will show how such considerations give rise to family multi-partite measures that agree on the holographic state, answering why the holographic states are special.

I present a consistent theory of classical systems coupled to quantum ones via the path integral formulation. In the classical limit, this is the path integral for stochastic processes like Brownian motion. We apply the formalism to general relativity, since it's reasonable to question whether spacetime should have a quantum nature given its geometric description. In contrast to perturbative quantum gravity, the pure gravity theory is formally renormalisable, and doesn't suffer from negative norm ghosts. This allows for both tabletop experiments and astrophyscical tests of the quantum nature of spacetime.

Tuesday, 27 August 2024

Recent work has produced a consistent picture of the holographic dual description of semi-classical gravity. I will describe this picture, several applications of this picture including the factorization puzzle and the information paradox, and some open questions.

The entanglement negativity is a useful measure of quantum entanglement in bipartite mixed states. The holographic dual of this entanglement measure has been controversial with calculations based on CFT techniques conflicting with calculations in random tensor networks (RTNs) that predict replica symmetry breaking. In this talk, I will argue that replica symmetry is broken for general holographic states. The argument involves relating the entanglement negativity to the 1/2 Renyi entropy of a doubled state. In order to compute it holographically, I will also discuss a modified cosmic brane proposal for computing Renyi entropies for n<1. I will comment on the differences with previous CFT calculations as well as those arising from RTNs with non-maximally entangled links.

Everything Everywhere All at Once: Holographic Entropy Inequalities, Entanglement Wedge Nesting, Topology of Error Correction, Black Holes, Cubohemioctahedron (and maybe the Toric Code)

Information-theoretic quantities such as Renyi entropies show a remarkable universality in their late-time behaviour across a variety of chaotic quantum many-body systems. Understanding how such common features emerge from very different microscopic dynamics remains an important challenge. In this talk, I will address this question in a class of Brownian models with random time-dependent Hamiltonians and a variety of different microscopic couplings. In any such model, the Lorentzian time-evolution of the n-th Renyi entropy can be mapped to evolution by a Euclidean Hamiltonian on 2n copies of the system. I will provide evidence that in systems with no symmetries, the low-energy excitations of the Euclidean Hamiltonian are universally given by a gapped quasiparticle-like band. These excitations give rise to the membrane picture of entanglement growth, with the membrane tension determined by their dispersion relation. I will establish this structure in a variety of cases using analytical perturbative methods and numerical variational techniques. I will also discuss qualitative differences in the behaviour of the second and third Renyi entropies. Overall, this structure provides an understanding of entanglement dynamics in terms of a universal set of gapped low-lying modes, which may also apply to systems with time-independent Hamiltonians.

I will discuss a new method to calculate entanglement entropy and entanglement negativity from field theories. This method provides a dictionary between correlation functions and entanglement measures for interacting Fermionic systems in and out of equilibrium. I will discuss application of this method to obtain interaction corrections to entanglement entropy of ground state of repulsively interacting Fermi gases.

We obtain the reflected entropy for bipartite mixed state configurations involving two disjoint and adjacent subsystems in a two dimensional boundary conformal field theory (BCFT2) in a black hole background. The bulk dual is described by an AdS3 black string geometry truncated by a Karch-Randall brane. The entanglement wedge cross section computed for this geometry matches with the reflected entropy obtained for the BCFT2 verifying the holographic duality. In this context, we also obtain the analogues of the Page curves for the reflected entropy and investigate the behaviour of the Markov gap.

In this talk, I will explore In AdS_2, states corresponding to slices of constant extrinsic curvature. We give an explicit construction of such states in JT gravity by studying the problem of non-smooth boundary conditions. The states are obtained by carrying out the appropriate Euclidean path integrals. We will discuss various checks on these states such as the classical limit, how the states constructed this way satisfy the WDW constraint etc.

Wednesday, 28 August 2024

We will introduce (standard) future operator algebras. We show that standard future algebras transform covariantly under the action of an emergent (universal cover of) PSL(2,R). In the case of generalized free fields with spectral densities corresponding to AdS_2 and higher dimensional eternal black holes, this symmetry corresponds to, respectively, the bulk AdS_2 and the conformal symmetry on the horizon.

What is the bulk Hilbert space of quantum gravity? In this paper, we resolve this problem in 2d JT gravity, both with and without matter, providing the first example of an explicit definition of a non-perturbative Hilbert space specified in terms of metric variables. The states are wavefunctions of the length and matter state, but with a non-trivial and highly degenerate inner product. We explicitly identify the null states, and discuss their importance for defining operators non-perturbatively. To highlight the power of the formalism we developed, we study the non-perturbative effects for two bulk linear operators that may serve as proxies for the experience of an observer falling into a two-sided black hole: one captures the length of an Einstein-Rosen bridge and the other captures the center-of-mass collision energy between two particles falling from opposite sides. We track the behavior of these operators up to times of order eSBH, at which point the wavefunction spreads to the complete set of eigenstates of these operators. If these observables are indeed good proxies for the experience of an infalling observer, our results indicate an O(1) probability of detecting a firewall at late times that is self-averaging and universal.

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.

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.

We discuss a bulk construction that has many of the features of the microstates of a one-sided large AdS black hole.

Humanity faces real and present problems. Our resources to address these problems are limited. It’s easy to think, then, that we should devote ourselves to our most promising solutions.

It’s easy, but it’s wrong.

The great paradox of scientific research is that pure exploration – research into deep questions motivated by pure curiosity, without concern for applications – is ultimately what transforms our lives in tangible, practical ways.

In this talk, I will speak not just as a physicist interested in puzzles of quantum entanglement and five-dimensional black holes, but as the director of an institute devoted to fundamental research. I make the case for blue-sky research, and for optimism about our shared future.

Thursday, 29 August 2024

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.

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.

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 complex extremal surfaces in these cases. We discuss physical principles that can be utilized to single out the physical contribution.

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.

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.

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 entangled states.

Friday, 30 August 2024

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.

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

We will discuss the study of quantum channel capacity of Gao-Jafferis-Wall traversable wormhole protocol using coherent information.

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 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.

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 strength controlled by measurement strength in the semiclassical limit and the system undergoes a MIPT analogous to well-known stochastic synchronization transition in classical systems.

Monday, 02 September 2024

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.

Tuesday, 03 September 2024

We construct baby universe corrected bulk black hole/ white hole orthonormal basis labeled by the geodesic length of timeslice in two sided black hole. Our construction gives manifestly well defined probability distribution for length as well as transition probability to a white hole. We compute these probability distributions perturbatively, and find that late time TFD state spreads over all BH/WH basis states, i.e. Susskind's grey hole, already at the second order in perturbation. We also comment on the inherent ambiguity in our construction of our geometric basis.

Wednesday, 04 September 2024

The eigenstate thermalization hypothesis (ETH) provides a sufficient condition for thermalization and equilibration from any initial states in isolated systems with a large number of degrees of freedom. One part of this statement is that for large systems, the diagonal matrix elements of typical observables in the Hamiltonian eigenstate basis, that is, the expectation values of the energy eigenstates, depend smoothly on the corresponding energy values. This statement is highly related to the fact that the variance of the energy eigenstate expectation values is small. Indeed, it is conjectured that this variance shows power-law decay with respect to the Hilbert space dimension.

On the other hand, in general relativity, it is expected that heavy objects undergo gravitational collapse. Additionally, it is known that gravitational systems with black holes exhibit maximally chaotic properties. By using the holographic principle, or specifically the AdS/CFT correspondence, these facts imply that holographic theories dual to higher-dimensional Einstein gravity will show chaotic behavior and also thermalization from high-energy states. Thus, we expect that holographic theories exhibit ETH, although there is no definitive proof for this.

In this talk, we discuss that the variance of the eigenstate expectation values of primary and descendant operators shows power-law decay with respect to the Hilbert space dimension. This fact is derived from the quantum mixing properties of holographic theories with black hole gravitational duals. We also discuss the consequences of this scaling on thermalization.

This talk is based on work in progress.