Talks

It has been proposed that microscopic black holes can catalyze decay of metastable false vacuum. The calculations of the decay rate existing in the literature make use of the Euclidean time formalism developed for equilibrium configurations. This is not the case, however, for a realistic black hole formed by gravitational collapse and emitting Hawking radiation. I will review the motivations to study black hole catalysis of vacuum decay, propose a general method to calculate the decay rate, and illustrate it on a two-dimensional toy model.

It has been shown that, despite being local, a perturbation applied to a single site of the one-dimensional XXZ model is enough to bring this interacting integrable spin-1/2 system to the chaotic regime. In this talk, we show that this is not unique to the XXZ model, but happens also to the spin-1/2 Ising model in a transverse field and to the spin-1 Lai-Sutherland chain. The larger the system is, the smaller the amplitude of the local perturbation for the onset of chaos. We focus on two indicators of chaos, the correlation hole, which is a dynamical tool, and the distribution of off-diagonal elements of local observables, which is used in the eigenstate thermalization hypothesis. Both methods avoid spectrum unfolding and can detect chaos even when the eigenvalues are not separated by symmetry sectors.

In this lecture we will show that the E8 and Leech lattices minimize energy of every potential function that is a completely monotonic function of squared distance (for example, inverse power laws or Gaussians). This theorem implies recently proven optimality of E8 and Leech lattices as sphere packings and broadly generalizes it to long-range interactions. The key ingredient of the proof is sharp linear programming bounds. To construct the optimal auxiliary functions attaining these bounds, we prove a new interpolation theorem. This is the joint work with Henry Cohn, Abhinav Kumar, Stephen D. Miller, and Danylo Radchenko.

The last decade has seen significant progress in our understanding of scattering in anti-de Sitter (AdS) space. Through the AdS/CFT correspondence, we can reformulate scattering processes in AdS in terms of correlation functions in Conformal Field Theory (CFT), which are sharply defined by the requirements of Conformal Symmetry, Unitarity and a consistent Operator Product expansion. Accordingly, numerous highly effective techniques for the study of scattering in AdS have been developed. This has been driven largely by the Conformal Bootstrap programme, which aims to carve out the space of consistent CFTs (and, in turn, quantum gravities in AdS space) principally through the three basic consistency requirements above. In this talk I will describe some steps towards extending some of these techniques and results to boundary correlators in de Sitter (dS) space. Compared to AdS, we have little grasp of the properties required of consistent correlation functions in Euclidean CFTs dual to physics in dS. The boundaries at infinity in dS are space-like with no standard notion of locality and time, so the basic criteria that underpin the Conformal Bootstrap programme do not directly apply to the corresponding programme in dS, the so-called Cosmological bootstrap. I will show how boundary correlators in AdS and dS can be placed on a similar footing by introducing a Mellin-Barnes representation in momentum space, providing a framework that could facilitate bridging the gap between the Conformal and Cosmological bootstrap programmes. I will then discuss how the Mellin-Barnes representation itself can be a useful tool to study boundary correlators both in AdS and dS.

Following the recommendation of the Update of the European Strategy for Particle Physics and in view of rising interest shown in the US Snowmass process, a new International Muon Collider Collaboration is forming, hosted at CERN. The presentation will introduce the muon collider concept, the reason for the renewed interest and the main challenges and opportunities.

Large surveys of the positions of galaxies in the Universe are becoming increasingly powerful to shed light on some of the unsolved problems of cosmology, including the question of what caused the early Universe to expand. The analysis of the data is challenging, however, because the signal is small, the data is difficult to model, and its probability distribution is not fully known. I will present some recent ideas to approach these challenges.

The extension of many-body quantum dynamics to the non-unitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between space and time on one hand, and unitarity and non-unitarity on the other, can be used to realize steady state phases of non-unitary dynamics that exhibit a rich variety of behavior in their entanglement scaling with subsystem size --- from logarithmic to extensive to fractal. We show how these outcomes in non-unitary circuits (that are ``spacetime-dual" to unitary circuits) relate to the growth of entanglement in time in the corresponding unitary circuits, and how they differ, through an exact mapping to a problem of unitary evolution with boundary decoherence, in which information gets ``radiated away'' from one edge of the system. In spacetime-duals of chaotic unitary circuits, this mapping allows us to uncover a non-thermal volume-law entangled phase with a logarithmic correction to the entropy distinct from other known examples. Most notably, we also find novel steady state phases with fractal entanglement scaling, $S(\ell) \sim \ell^{\alpha}$ with tunable $0 < \alpha < 1$ for subsystems of size $\ell$ in one dimension. These fractally entangled states add a qualitatively new entry to the families of many-body quantum states that have been studied as energy eigenstates or dynamical steady states, whose entropy almost always displays either area-law, volume-law or logarithmic scaling. We also present an experimental protocol for preparing these novel steady states with only a very limited amount of postselection via a type of ``teleportation" between spacelike and timelike slices of quantum circuits.

The prepare-and-measure scenario is ubiquitous in physics. However, beyond the paradigmatic example of dense coding, there is little known about the correlations p(b|x,y) that can be generated between a sender with input x and a receiver with input y and outcome b. Contrasting dense coding, we show that the most powerful protocols based on qubit communication require high-dimensional entanglement. This motivates us to systematically characterise the sets of correlations achievable with classical and quantum communication, respectively, assisted by a potentially unbounded amount of entanglement. We obtain two different SDP hierarchies for both the classical and quantum case: one based on NPA and one based on informationally-restricted correlations. In the talk, I will discuss the advantages and drawbacks of each, and show that they can be used obtain tight or nearly-tight bounds on in several concrete case studies. As examples of applications, these new tools are used to construct device-independent dimension witnesses robust to unbounded shared entanglement and several resource inequalities for quantum communications.

I will consider the phase space at null-infinity from the r\rightarrow\infty limit of a quasi-local phase space for a finite box with a boundary that is null. This box will serve as a natural IR regulator. To remove the IR regulator, I will consider a double null foliation together with an adapted Newman--Penrose null tetrad. The limit to null infinity (on phase space) is obtained in the limit where the boundary is sent to infinity. I will introduce various charges and explain the role of the corresponding balance laws. The talk is based on the paper: arXiv:2012.01889.