Week 04.11.2024 – 10.11.2024

Scattering amplitudes provide crucial theoretical input in collider and gravitational wave physics, and at the same time exhibit a remarkable mathematical structure. These lectures will introduce essential concepts and modern techniques exploiting this structure so as to efficiently compute amplitudes and their building blocks, Feynman integrals, in perturbation theory. We will start by decomposing gauge theory amplitudes into simpler pieces based on colour and helicity information. Focusing on tree level, we will then show how these may be determined from their analytic properties with the help of Britto-Cachazo-Feng-Witten recursion. Moving on to loop level, we will define the the class of polylogarithmic functions amplitudes and integrals often evaluate to, and explain their properties as well as relate them to the universal framework for predicting their singularities, known as the Landau equations. Time permitting, we will also summarise the state of the art in the calculation of the aforementioned singularities, and their intriguing relation to mathematical objects known as cluster algebras.

We do not understand 95% of our Universe. 63% of this unknown is dark energy (or a cosmological constant), which drives the accelerated expansion of the universe and 27% is dark matter, an additional matter component which clumps together to form large halos around visible galaxies. These two dominating components of the universe have only been observed through their gravitational effects, and both represent the failure of our standard models of particle physics and gravity to explain cosmology from a fundamental physics standpoint. In this talk I will focus on the introduction of new light scalar fields which have been suggested as possible explanations for dark matter and the accelerated expansion of the universe. I will show examples of the unusual phenomenology that can arise in such theories, and explain why properties of macroscopic objects, such as density and compactness, are important in understanding how to detect them. I'll then show how this leads to new opportunities for precision laboratory measurements to shed light on this type of new physics.

I will revisit the problem of defining an invariant notion of brane tension, analogous to the ADM mass, in a theory of gravity. I will propose two natural definitions, a gravitational and an inertial tension, in terms of asymptotic data akin to that of a Defect CFT. I will illustrate these definitions with various examples, and present the evidence why for supersymmetric branes the two tensions must be equal.

I will talk about Yang-Mills theory on four dimensional Anti-de Sitter space. The Dirichlet boundary condition cannot exist at arbitrarily large radius because it would give rise to colored asymptotic states in flat space. This implies a deconfinement-confinement transition as the radius is increased. I will show hints on the nature of this transition obtained in 2407.06268 using perturbation theory. The results favor the scenario of merger and annihilation as the most promising candidate for the transition.