Talks

I will discuss the properties, and constraints on, new light

particles, which appear in many extensions of the Standard Model. An

especially well motivated example is the QCD axion, and I will show how

its mass and couplings can be extracted at high precision. I will also

discuss its properties at finite temperature, and possible distinguishing

features if it makes up dark matter. More generally, strong constraints on

the couplings of new light particles to the Standard Model come from their

production in the hot cores of stars, and the effect on stellar cooling.

The large electron density in stellar cores gives large thermal effects,

and I will show how these can parametrically change the production rates

compared to a 'tree level' calculation.

We argue that moduli stabilization severely constrains the evolution following transitions between weakly coupled de Sitter vacua and can induce a strong selection bias towards inflationary cosmologies. We carefully discuss gravitational vacuum decays and resolve a naive sign ambiguity in the exponential of the decay rate. Equipped with this clear understanding of vacuum decay we then turn towards constraints on the cosmological evolution after transitions in weakly coupled flux compactifications. The energy density of domain walls between vacua typically destabilizes Kahler moduli and triggers a runaway towards large volume. This decompactification phase can collapse the new de Sitter region unless inflation lasts for more than roughly 60 efolds. High scale inflation is vastly favored. Our results illustrate the necessity to understand inflationary initial conditions at least at a basic level, before making predictions in the landscape.

In order to solve the problem of quantum gravity, we first need to pose the problem. In this talk I will argue that the problem of quantum gravity arises already in the domain of quantum mechanics and the relativity principle. Specifically, the relativity principle implies that the concept of inertial motion should extend also to those systems that are in quantum superpositions of inertial motions. By contrast, relativistic quantum field theory only considers the point of view of classical observers in states of definite relative motion (i.e. the observers of a quantum field do not include inertial observers in quantum superpositions). The problem is that, if we extend the class of inertial observers to include quantum observers, the manifold of local events becomes ill-defined, as `locality' itself becomes an observer-relative property of an event. Thus, the Relativity Principle and the Superposition Principle are jointly opposed to the concept of a space-time manifold of local events, and our understanding of relativistic quantum theory needs to be revised before gravity even enters the picture.

In this talk, I will address a major conceptual and technical concern of non-perturbative quantum gravity: the quantum superposition of causal structures of space-times. I will discuss a class of theories that can address the problem, their flaws, and their relation to general relativity.

The Wigner-Eckart theorem is a well known result for tensor operators of SU(2) and, more generally, any compact Lie group. I will show how it can be generalised to arbitrary Lie groups, possibly non-compact. The result relies on the knowledge of recoupling theory between finite-dimensional and arbitrary admissible representations, which may be infinite-dimensional; the particular case of the Lorentz group will be studied in detail. As an application, the Wigner-Eckart theorem will be used to construct an analogue of the Jordan-Schwinger representation, previously known only for finite-dimensional representations of the Lorentz group, valid for infinite-dimensional ones.

I will describe some of the recent progress in quantum query complexity, including super-quadratic separations between classical and quantum measures for total functions, a better understanding of the power of some lower bound techniques, and insight into when we should expect exponential quantum speedups for partial functions.

Recent explorations of the space of quantum field theories have provided novel topological and geometric information about this space. This voyage has resulted in the solution of some long-standing questions:  the computation of sought-after topological invariants (Gromov-Witten invariants) by a new physics-based approach, the first instance of exact correlation functions in a four-dimensional QFT and the unearthing of the action of dualities on the basic observables of three dimensional gauge theories.