...
- 30.04., Tomas Brauner (UiS): Topology of spontaneous symmetry breaking, emergent higher-form and higher-group symmetries
Abstract: Spontaneous breaking of a continuous global symmetry implies as a rule the existence of new, emergent symmetries, associated with the topology of the vacuum manifold. These may take the form of ordinary symmetries associated to a conserved current and localized charged excitations, or higher-form symmetries, acting on extended topological defects. I will give a brief introduction to the above-mentioned concepts, and then show how higher-form symmetries can be combined into a more general mathematical structure still, referred to as higher-group symmetry. This is a concept that has recently attracted attention in the high-energy theory community. It however turns out to be also relevant for systems as mundane as superfluid mixtures.
slides - 07.05., Magnus Malmquist (NTNU): Polarization Sums and Unitarity in QCD
Abstract: One of the first techniques one encounters when learning quantum field theory is the method of replacing the sum over photon polarizations by minus the metric tensor. This is not an equality; instead the QED Ward identity ensures that the replacement gives the correct result. We ask the simple question of whether this replacement can be made in a non-abelian theory like QCD. The answer is "yes, we can". Using unitarity we explain how the method should be applied in QCD, which requires considering external Faddeev-Popov ghosts. Understanding the procedure of replacing the polarization sum by minus the metric tensor then leads us to Slavnov-Taylor identities which are a core stone of the mathematical consistency of QCD.
slides
- 21.05., Magdalena Eriksson (NTNU, UiS): Quantum corrections to inflation
Abstract: The theory of cosmic inflation solves the problems of Big Bang cosmology and provides an explanation to the origin of the cosmic microwave background (CMB) radiation. Inflation is often modelled with a scalar field slowly rolling down some potential in FRLW spacetime. In cosmological perturbation theory one perturbs this inflaton field as well as the FRLW metric, and these perturbations can be related to the temperature fluctuations observed in the CMB. In this talk I give an introduction to inflationary cosmology and cosmological correlation functions. I introduce the concept of corrections to these correlation functions and how they can affect the inflationary dynamics. In particular I differentiate between corrections to cosmological observables, i.e. n-point correlation functions, and corrections to the evolving inflaton field and background metric. Corrections to the evolution equations can be viewed as corrections to the slow-rolling parameters, which also enter into observables.
...