Contact Name: Barbara Simoni
Abstract:
It has become apparent in modern approaches attempting to quantise gravity that extended, non-point-like, fundamental objects are likely to play an important role at high energy scale. We also know that in this set-up one is commonly faced with novel geometries, as the building blocks inhabit and probe non-commutative backgrounds. Theories constructed via the world-volumes of such extended objects are then expected to exhibit "higher gauge invariance", i.e. invariance under the reparametrisation of surfaces and volumes, rather than just ordered paths. We will see how category theory is used in tackling the issue in a short introduction to the mathematical techniques involved, before passing on to some examples of models built in this framework. Though the mathematical tools are well developed, the associated physics are still far from being well understood and offer a fertile ground for research into some of the fundamental implications of quantum gravity.