Abstract:
A sigma model of a manifold $X$ is a theory of harmonic maps
from a Riemann surface to $X$, and, at the same time, an important
example of (classical and quantum) field theory. Sigma models of
complex homogeneous spaces have especially remarkable
properties. For example, it turns out that Grassmannian (or, more
generally, flag manifold) sigma models may be naturally formulated
in terms of symplectic structures on nilpotent orbits of the
respective complex groups. These orbits are quiver varieties, and,
as such, carry natural variables, which are particularly useful for
the quantum theory of sigma models. Apart from introducing the
general circle of relevant ideas, I will discuss one-loop quantum
corrections and, possibly, supersymmetric generalizations.