Mitchell Institute for Fundamental Physics & Astronomy
College Station, Texas 77843
This talk has two parts. In part I, Bei Jia will discuss **N=1** nonlinear sigma models coupled to **N=1** vector multiplets on four-manifolds, via a decoupling gravity procedure from **4d N=1** supergravity coupled to gauge fields. One of the results is that in one class of these models, the Fayet-Iliopoulos parameters will need to vanish. Furthermore, he will discuss the appearance of affine bundles in these theories, which is the rigid supersymmetric analog of the Bagger-Witten line bundle after decoupling from gravity.
In part II, he will discuss general **N=(2,2)** nonlinear sigma models of both chiral multiplets and twisted chiral multiplets on **S2**. In contrast to the four-dimensional cases, there is no further constraint needed on the target space, except the appearance of a holomorphic Killing vector field, representing the vector like **U(1)_R** part of the **N=(2,2)** supersymmetry algebra on **S2**. He will also discuss the observation that those curvature coupling terms in our Lagrangian lead to the absence of the usual symmetry between chiral multiplets and twisted chiral multiplets on **R^2**, as well as the usual topological twists.