Localizing non-linear N=(2,2) supersymmetric sigma model on sphere

I will tell about supersymmetric sigma models with a Kaehler target space on a two-dimensional sphere. It turns out that in addition to the A and B models on the sphere, it is possible to formulate another cohomological field theory that calculates the observables in some subsector of the original sigma model. With the help of localization in this theory, I will show that it is possible to calculate the part of the effective action corresponding to the Kaehler parameters. It can be seen that this result coincides with what is expected from the calculations in the gauge sigma model in accordance with the "hypothesis" of JKLMR (Jockers et al).