Abstract :
We consider the effect of curved two-dimensional space-time on Wittenʹs N = 2 supersymmetric sigma models interpolating Calabi-Yau hypersurfaces to Landau-Ginzburg models. In order for the former models to have significant connection to superstring theory, only the N = (1, 1) or N = (1, 0) part of the total N = (2, 2) world-sheet supersymmetry is made local. With the N = (1, 0) local supersymmetry, the nice feature of the hypersurface sigma-model with global supersymmetry interpolating the Calabi-Yau and Landau-Ginzburg models is maintained. In the case of the N = (1, 1) local supersymmetry, the elimination of a scalar auxiliary field for supergravity deletes the kinetic term of a vector in the vector multiplet, invalidating extrapolations between the two models. We overcome this problem by adding an extra U(1) vector multiplet. Our results indicate that the correspondence between the Calabi-Yau and Landau-Ginzburg models on curved two-dimensions is valid both for N = (1, 0) and N = (1, 1) local supersymmetries. The coupling of N = (2, 2) vector multiplets to other multiplets with N = (1, 1) local supersymmetry is also developed.
