Seminarium KMMF "Teoria Dwoistości"

In the first part of the talk we will explain the notion of a singularRiemannian foliation (SRF) as a mathematical generalization of isometricgroup actions on a Riemannian manifold (M,g). We will relate this inparticular to constrained dynamical systems on T*M, where the definingcondition between the foliation on M and the metric g appears as acompatibility condition of first class constraints with the naturalHamiltonian flow generated by g. In the second part of the talk we will show how to construct gaugetheories beyond the standard use of group actions. A simple prototype ofsuch a gauge theory is the Poisson sigma model, which we will brieflyrecall in this context. However, this theory is defined in twodimensions only and, more importantly, is topological (thus in somesense "unphysical"). We show how the use of SRFs permits to constructgauge theories in arbitrary spacetime dimensions with propagatingdegrees of freedom. Replacing the notion of a quadratic Lie algebra,used to define standard Yang-Mills theories, by quadratic Liealgebroids, we will be led to what we call Curved Yang-Mills-Higgs GaugeTheories as a generalization of the Yang-Mills-Higgs sector of the Standard Model of particle physics. To join our online seminar, use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09