Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories

摘要: We consider three-dimensional $ \mathcal{N}=2 $ superconformal field theories on a threesphere and analyze their free energy F as function of background gauge supergravity fields. A crucial role is played by certain local terms in these fields, including several Chern-Simons terms. The presence clarifies number subtle properties . This understanding allows us to prove the -maximization principle. It also explains why computing via localization leads complex answer, even though we expect it be real unitary theories. discuss corollaries our results comment relation -theorem.