Topological Chern-Simons sigma model

We consider topological twisting of recently constructed Chern-Simons-matter theories in three dimensions with N = 4 or higher supersymmetry. We enumerate physically inequivalent twistings for each N, and find two different twistings for N = 4, one for N = 5, 6, and four for N = 8. We construct the two types of N = 4 topological theories, which we call A/B-models, in full detail. The A-model has been recently studied by Kapustin and Saulina. The B-model is new and it consists solely of a Chern-Simons term of a complex gauge field up to BRST-exact terms. We also compare the new theories with topological Yang-Mills theories and find some interesting connections. In particular, the A-model seems to off er a new perspective on Casson invariant and its relation to Rozansky-Witten theory.