Date: 
October 2, 2008, 15:30  17:00 
Place: 
Seminar Room at IPMU Prefab. B, Kashiwa Campus of the University of Tokyo 
Speaker: 
Sven Bjarke Gudnason (Univ. of Pisa) 
Title: 
SO and USp K\"ahler and HyperK\"ahler Quotients and Lumps

Abstract: 
The properties of supersymmetric gauge theories in the Higgs phase at
low energies can appropriately be studied by means of a nonlinear sigma
model, which has the target space being K\"ahler for N=1 supersymmetric
models and hyperK\"ahler for N=2 models. By construction of the
K\"ahler and hyperK\"ahler quotients for the gauge theories with SO and
USp gauge symmetries, we obtain the explicit metrics and their K\"ahler
potentials of their corresponding manifolds, which are equivalent to the
moduli space of vacua of the original gauge theories. Furthermore, we
develop an expansion formula to make use of the obtained metrics from
which we also calculate the curvatures of the manifolds.
The last scope is to study the lumps in the nonlinear sigma models and
their effective descriptions. In this connection we introduce the moduli
matrix formalism and make a connection with the moduli space of vortices
from the moduli space of lumps.
