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**.
At short distances the Susy transformations are part of the at space superalgebra. The theory is invariant under some Supersymmetry. We want to place it on a manifold (M,g) so that: The short distance limit of the theory is unaected. In part II, he will discuss general **N=(2,2)** nonlinear sigma models of both chiral multiplets and twisted chiral multiplets on **S2**. Susy on Curved Manifolds Consider a supersymmetric theory in at space. Why Susy in curved space Allows to compute exactly many interesting observables such as. Quantum field theory in curved spacetime (QFTCS) is a field of study that focuses on problems that arise when considering a quantum field on a fixed. 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. Guido Festuccia Rigid Supersymmetry in Curved Superspace. One of the results is that in one class of these models, the Fayet-Iliopoulos parameters will need to vanish. 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. Following the idea of obtaining supersymmetry on a curved manifold by taking rigid limit of suitable supergravity 48, various developments took place to understand the relation between. 2d (2,2) curved superspace For rigid SUSY in curved spacetime use supergravity Festuccia, NS Simplification in 2d (locally) pick conformal gauge 2 for SUSY (locally) pick superconformal gauge use flat space expressions with explicit ’s Two kinds of (2,2) supergravities.
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