N=2supersymmetric sigma models and D-branes

Abstract

We study D-branes of $N=2$ supersymmetric sigma models. Supersymmetric nonlinear sigma models with 2-dimensional target space have $p$-dimensional branes ($p=0,1,2$), which are realized as $A$- or $B$-type supersymmetric boundary conditions on the world sheet. When we embed the models in the string theory, the K\"ahler potential is restricted and leads to a 2-dimensional black hole metric with a dilaton background. The D-branes in this model are supersymmetric cycles and our analysis is consistent with that of conjugacy classes. The generalized metrics with $\mathrm{U}(n)$ isometry are proposed and dynamics on them are realized by linear sigma models. We investigate D-branes of the linear sigma models and compare the results with those in the nonlinear sigma models.