We introduce a symplectic structure on the space of connections in a G-principal bundle over a four-manifold and the Hamiltonian action on it of the group of gauge transformations which are trivial on the boundary. The symplectic reduction becomes the moduli space of flat connections over the manifold. On the moduli space of flat connections we shall construct a hermitian line bundle with conne...

We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons term on a flat spatial two-torus. The Witten index may be computed in the weak coupling limit, where the ground state wave-functions localize on the moduli space of flat gauge connections. We perform such computations by considering this moduli space as an orbifold of a certain flat complex torus. Our results agree with ...

For a compact, connected Lie group G, we study the moduli of pairs (Σ,E), where Σ is a genus g Riemann surface and E →Σ is a flat G-bundle. Varying both the Riemann surface Σ and the flat bundle leads to a moduli space Mg , parametrizing families Riemann surfaces with flat G-bundles. We show that there is a stable range in which the homology of Mg is independent of g. The stable range depends o...

Abstract Kagome lattices host flat bands due to their frustrated lattice geometry, which leads destructive quantum interference of electron wave functions. Here, we report imaging the kagome band localization in real-space using scanning tunneling microscopy. We identify both Fe 3 Sn layer and 2 honeycomb with atomic resolution antiferromagnet FeSn. On lattice, at energy determined by angle res...

All maximally superintegrable Hamiltonian systems in three-dimensional flat space derived the work of Evans [Phys. Rev. A 41, 5666–5676 (1990)] are shown to possess hidden symmetries leading their linearization, likewise two-dimensional as Gubbiotti and Nucci [J. Math. Phys. 58, 012902 (2017)]. We conjecture that even minimally have make them linearizable.

Complex and interesting electromagnetic behavior can be found in spaces with non-flat topology. When considering the properties of an electromagnetic medium under an arbitrary coordinate transformation an alternative interpretation presents itself. The transformed material property tensors may be interpreted as a different set of material properties in a flat, Cartesian space. We describe the c...