Noriaki Ikeda
Q-manifolds and sigma models
We discuss relations of Q-manifolds (differential graded manifolds) to physical theories. A Q-manifold is called a QP-manifold if it has a compatible symplectic structure. One of main applications is the BRST-BV formalism of gauge theories. We discuss sigma models. There are two types of sigma models, topological ones and non-topological ones. In topological versions, ASKZ sigma models are directly constructed from Q-manifolds, which give a large class of topological sigma models. We discuss a generalization of AKSZ sigma models by deforming a Q-structure on the mapping space. Next, we discuss a non-topological version, a gauged nonlinear sigma model (GNLSM). Though physicists have constructed GNLSMs by hand, a Q-manifold structure naturally appears in this construction and we obtain a theoretical construction of GNLSMs.
