supersymmetric action on the curved space of interest, solve Killing spinor equations. 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. 3 Entanglement Entropy and Conformal Collider Physics in 2D CFTs. 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**. The fields of this theory are: Elfbein ENB, N curved space index. Bershadsky: Topological reduction of 4D super Yang-Mills to 2D sigma models. Thus the number of supersymmetries N in four dimensions is N 12r 2D/2. In part II, he will discuss general **N=(2,2)** nonlinear sigma models of both chiral multiplets and twisted chiral multiplets on **S2**. Berkovits: New space-time supersymmetric methods for the superstring M.
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. We study the consequences of unbroken rigid supersymmetry of four-dimensional field theories placed on curved manifolds.
One of the results is that in one class of these models, the Fayet-Iliopoulos parameters will need to vanish. C., Zaffaroni, A.: Extended supersymmetry on curved spaces.
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. arXiv:1312.2684 Gadde, A., Gukov, S.: 2d index and surface operators.
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