A-twisted Landau-Ginzburg models
  In this paper we discuss correlation functions in certain A-twisted Landau-Ginzburg models. Although B-twisted Landau-Ginzburg models have been discussed extensively in the literature, virtually no work has been done on A-twisted theories. In particular, we study examples of Landau-Ginzburg models over topologically nontrivial spaces - not just vector spaces - away from large-radius limits, so that one expects nontrivial curve corrections. By studying examples of Landau-Ginzburg models in the same universality class as nonlinear sigma models on nontrivial Calabi-Yaus, we obtain nontrivial tests of our methods as well as a physical realization of some simple examples of virtual fundamental class computations. 
Josh Guffin and Eric Sharpe