Exact effective central charges for a family of 3d superconformal field theories

We conjecture an exact formula for the effective central charge, ceff, of a family of three- dimensional superconformal field theories related to Chern-Simons theory on a three-manifold by the 3d-3d correspondence. The formula determines ceff , which governs the growth of a protected sector of states in the conformal theory, in terms of the dimension of a particular space of modular forms. We confirm our approach by checking against known results computed through resurgent continuation.