Particles and Fields

General relativity in three spacetime dimensions is a simplified model of gravity, possessing no local degrees of freedom, yet rich enough to admit black-hole solutions and other phenomena of interest. In the presence of a negative cosmological constant, the asymptotically anti–de Sitter (AdS) solutions admit a symmetry algebra consisting of two copies of the Virasoro algebra, with central charge inversely proportional to Newton’s constant. The study of this theory is greatly enriched by the AdS/CFT correspondence, which in this case implies a relationship to two-dimensional conformal field theory. General aspects of this theory can be understood by focusing on universal properties such as symmetries. The best understood examples of the AdS3/CFT2 correspondence arise from string theory constructions, in which case the gravity sector is accompanied by other propagating degrees of freedom. A question of recent interest is whether pure gravity can be made sense of as a quantum theory of gravity with a holographic dual. Attempting to answer this question requires making sense of the path integral over asymptotically AdS3 geometries.

Calabi-Yau spaces, or Kähler spaces admitting zero Ricci curvature, have played a pivotal role in theoretical physics and pure mathematics for the last half century. In physics, they constituted the first and natural solution to compactification of superstring theory to our 4-dimensional universe, primarily due to one of their equivalent definitions being the admittance of covariantly constant spinors. Since the mid-1980s, physicists and mathematicians have joined forces in creating explicit examples of Calabi-Yau spaces, compiling databases of formidable size, including the complete intersecion (CICY) data set, the weighted hypersurfaces data set, the elliptic-fibration data set, the Kreuzer-Skarke toric hypersurface data set, generalized CICYs, etc., totaling at least on the order of 10 10 manifolds. These all contribute to the vast string landscape, the multitude of possible vacuum solutions to string compactification. More recently, this collaboration has been enriched by computer science and data science, the former in bench-marking the complexity of the algorithms in computing geometric quantities, and the latter in applying techniques such as machine learning in extracting unexpected information. These endeavours, inspired by the physics of the string landscape, have rendered the investigation of Calabi-Yau spaces one of the most exciting and interdisciplinary fields.

With the huge success of quantum electrodynamics (QED) to describe electromagnetic interactions in nature, several attempts have been made to extend the concept of gauge theories to the other known fundamental interactions. It was realized in the late 1960s that electromagnetic and weak interactions can be described by a single unified gauge theory. In addition to the photon, the single mediator of the electromagnetic interaction, this theory predicted new, heavy particles responsible for the weak interaction, namely the W and the Z bosons. A scalar field, the Higgs field, was introduced to generate their mass. The discovery of the mediators of the weak interaction in 1983, at the European Center for Nuclear Research (CERN), marked a breakthrough in fundamental physics and opened the door to more precise tests of the Standard Model. Subsequent measurements of the weak boson properties allowed the mass of the top quark and of the Higgs Boson to be predicted before their discovery. Nowadays, these measurements are used to further probe the consistency of the Standard Model, and to place constrains on theories attempting to answer still open questions in physics, such as the presence of dark matter in the universe or unification of the electroweak and strong interactions with gravity.

A quantum quench is a process in which a parameter of a many-body system or quantum field theory is changed in time, taking an initial stationary state into a complicated excited state. Traditionally “quench” refers to a process where this time dependence is fast compared to all scales in the problem. However in recent years the terminology has been generalized to include smooth changes that are slow compared to initial scales in the problem, but become fast compared to the physical scales at some later time, leading to a breakdown of adiabatic evolution. Quantum quench has been recently used as a theoretical tool to study many aspects of nonequilibrium physics like thermalization and universal aspects of critical dynamics. Relatively recent experiments in cold atom systems have implemented such quench protocols, which explore dynamical passages through critical points, and study in detail the process of relaxation to a steady state. On the other hand, quenches which remain adiabatic have been explored as a useful technique in quantum computation.

Quantum field theory (QFT) in six dimensions is more challenging than its four-dimensional counterpart: most models tend to become ill-defined at high energies. A combination of supersymmetry and string theory has yielded many QFTs that evade this problem and are low-energy effective manifestations of conformal field theories (CFTs). Besides the usual vector, spinor and scalar fields, the new ingredients are self-dual tensor fields, analogs of the electromagnetic field with an additional spacetime index, sometimes with an additional non-Abelian structure. A recent wave of interest in this field has produced several classification results, notably of models that have a holographic dual in string theory and of models that can be realized in F-theory. Several precise quantitative checks of the overall picture are now available, and give confidence that a full classification of all six-dimensional CFTs may be at hand.conformal field theories, supersymmetry, extra dimensions, holography, string theory, D-branes, F-theory

Conformal field theories (CFTs) have a wide range of experimental and theoretical applications. They describe classical and quantum critical phenomena, low (or high) energy limits of quantum field theories, and even quantum gravity via the Anti-de Sitter space/CFT correspondence (AdS/CFT). Most interesting, CFTs are strongly interacting and difficult to analyze. The Conformal Bootstrap program is an approach that exploits only basic consistency conditions of CFTs, such as unitarity, locality, and symmetry, encoded into a set of bootstrap equations. The hope is that such conditions might be strong enough to uniquely determine the full set of consistent theories. This philosophy was first used successfuly in the 1980s to analytically determine and classify large classes of critical phenomena in two spatial dimensions. Starting from 2008, major developments have allowed the exploration of CFTs in more general spacetime dimension. The key breakthrough was to realize that one could exploit methods from linear and semidefinite optimization theory to analyze the bootstrap equations and obtain strong, universal constraints on the space of CFTs. The Conformal Bootstrap has led to a number of important results in the study of CFTs. One of the main outcomes consists of general bounds on the data defining a CFT, such as critical exponents and operator–product expansion coefficients. This has been done for a number of contexts, such as different space-time dimensions, global symmetry groups, and various amounts of supersymmetry. More remarkably, this approach not only leads to general results on the space of theories but is also powerful enough to give extremely precise determinations of the properties of specific models, such as the critical exponents of the critical 3d Ising and O(2) models. Finally the conformal-bootstrap program also includes the formal study and non-perturbative definition of CFTs and their observables. These include not only the study of Euclidean correlation functions but also a study of their properties in Lorentzian signature; the study of defects, interfaces, and boundary conditions; finite temperature; and connections to the AdS/CFT correspondence.

Deepening our knowledge of the partonic content of nucleons and nuclei represents a central endeavor of modern high-energy and nuclear physics, with ramifications in related disciplines, such as astroparticle physics. There are two main scientific drivers motivating these investigations of the partonic structure of hadrons. On the one hand, addressing fundamental open issues in our understanding of the strong interaction, such as the origin of the nucleon mass, spin, and transverse structure; the presence of heavy quarks in the nucleon wave function; and the possible onset of novel gluon-dominated dynamical regimes. On the other hand, pinning down with the highest possible precision the substructure of nucleons and nuclei is a central component for theoretical predictions in a wide range of experiments, from proton and heavy-ion collisions at the Large Hadron Collider to ultra-high-energy neutrino interactions at neutrino telescopes.