Scientific Series

Black Hole Entropy is a well established concept and arises naturally once one realises that black holes are characterised by a temperature. Boltzmann established that entropy can be regarded as the logarithm of the density of states function. However, black hole uniqueness theorems appeared to indicate that black holes have no hair. I will describe a loophole in the no-hair theorems and how black holes can have an infinite set of charges related to "large" gauge transformations. I will then use these ideas to show that on sections of the horizon there is a holographic conformal field theory. The temperature of this conformal theory means that it has a statistical entropy that reproduces the Hawking formula. The implications of this for the black hole information paradox will be briefly described.
 

The mixing time of Markovian dissipative evolutions of open quantum many-body systems can be bounded using optimal constants of certain quantum functional inequalities, such as the logarithmic Sobolev constant. For classical spin systems, the positivity of such constants follows from a mixing condition for the Gibbs measure, via quasi-factorization results for the entropy.

Inspired by the classical case, we present a strategy to derive the positivity of the logarithmic Sobolev constant associated to the dynamics of certain quantum systems from some clustering conditions on the Gibbs state of a local, commuting Hamiltonian. In particular we address this problem for the heat-bath dynamics in 1D and the Davies dynamics, showing that the first one is positive under the assumptions of a mixing condition on the Gibbs state and a strong quasi-factorization of the relative entropy, and the second one under some strong clustering of correlations.

Global symmetries and gauge symmetries have played a crucial role in physics.  The idea of duality demonstrates that gauge symmetries can be emergent and might not be fundamental.  During the past decades it became clear that the circle of ideas about emergent gauge symmetries and duality is central in different branches of physics including Condensed Matter Physics, Quantum Field Theory, and Quantum Gravity.   We will review these developments, which highlight the unity of physics.

Thanks to the Lanczos algorithm, the Hamiltonian dynamics of any operator can be written as a hopping problem on a semi-infinite one-dimensional chain. Our hypothesis states that the hopping strength grows linearly down the chain, with a universal growth rate $\alpha$ that is an intrinsic property of the system. This leads to an exponential motion of the operator down the chain, capturing the irreversible process of simple operators inevitably evolving into complex ones. This exponential growth exists for generic quantum systems, even away from large-$N$ or semiclassical limits. In fact, $\alpha$ gives an upper bound for the exponential growth rate of a large class of operator complexity measures, including out-of-time-order correlations. As a result, we conjecture a new bound on Lyapunov exponents $\lambda_L \leq 2 \alpha$, which generalizes the known universal low-temperature bound $\lambda_L \leq 2 \pi T$. We illustrate the hypothesis in paradigmatic examples such as non-integrable spin chains, the $q$-SYK model, and chaotic coupled top models, and show that some of them saturate the conjectured bound.

There is a fundamental tension between what string theory computes (S-matrix elements) and what you can compute in QFT on a time-dependent backgrounds (real time operator expectation values). The prescription for computing time dependent expectation values in QFT involves a path integral defined on a closed time path, known as the Keldysh contour. In this talk, we'll discuss how a worldsheet formulation of string theory must perceive the Keldysh contour and how this modifies critical string theory at tree level in the string coupling.

One of the best known open-source tools for studying numerical relativity is the Einstein Toolkit.  With it, you can simulate collisions of black holes and neutron stars, and study their horizons and gravitational waves. In this talk we learn more about what the Einstein Toolkit can do, how it works. An introductory, hands-on tutorial will follow.

Detecting light dark matter that interacts weakly with electromagnetism has recently become one of the benchmark goals of near-term and futuristic direct detection experiments. In this talk, I will discuss an alternative technique to directly detecting such particles below the GeV-scale. The approach involves distorting the local flow of dark matter with time-varying fields and measuring these distortions with shielded resonant detectors, such as LC circuits.

The relative entropy is a measure of the distinguishability of two quantum states. A great deal of progress has been made in the study of the relative entropy between an excited state and the vacuum state of a conformal field theory (CFT) reduced to a spherical region. For example, when the excited state is a small perturbation of the vacuum state, the relative entropy is known to have a universal expression for all CFT’s. Specifically, the perturbative relative entropy can be written as the symplectic flux of a certain scalar field in an auxiliary AdS-Rindler spacetime. Moreover, if the CFT has a semi-classical holographic dual, the relative entropy is known to be related to conserved charges in the bulk dual spacetime. In this talk, I will introduce a one-parameter generalization of the relative entropy which I will call 'refined' Renyi relative entropy. I will use this quantity to present a one-parameter generalization of the aforementioned known results about the relative entropy. I will also discuss a new family of positive energy theorems in asymptotically locally AdS spacetimes that arises from the holographic dual of the refined Rényi relative entropy.

Quantum complexity is a notion characterizing the universality of the entanglement arising from a quantum evolution. A universal evolution will result in a complex entanglement. At the same time, this also corresponds to small fluctuations and to unlearnability from the point of view of machine learning. All these aspects are connected to the different features of k-designs, which are under-samplings of the Hilbert space. 

We study the transition in complexity due to the doping of a quantum circuit by universal gates and show that the transition to complex entanglement can be obtained by just a single gate. 
These results are relevant for the notions of scrambling, quantum chaos, OTOCs and operator spreading.

We conjecture that the transition to 4−design, W-D and unlearnability are one and the same.

What is the ultimate fate of black holes? Since the discovery of Hawking evaporation process, the issue has been much discussed. Loop quantum gravity suggests that black hole could ultimately turn into white holes. In this talk, we investigate several possible mixed scenario where black holes first evaporate to a Planckian size before tunnelling to white holes. We build various spacetime models, taking Hawking backreaction into account, and we discuss some aspects of the expected phenomenology. Finally, we will draw the path for a full LQG amplitude computation that could lead to observational predictions.

I will describe some connections between the Eigenstate Thermalization Hypothesis (ETH), the entanglement structure of generic excited eigenstates of chaotic quantum systems ("EE", arXiv:1906.04295), and the "bound on chaos" limiting the growth rate of the out-of-time-order four-point correlator in such systems ("OTOC", arXiv:1906.10808).

Higher spin symmetries are gauge symmetries sourced by massless particles with spin greater than two. When coupled with diffeomorphism, they give rise to higher spin gravity. After a review on higher spin gravity, I will discuss its holography and its embedding in the string theory. Finally I will talk about some applications of higher spin symmetry, both in string theory and in QFT.