We present an overview of the recently obtained results for prospects for light dark matter search in experiments at the future Super c-tau factory in models of a leptophilic scalar and a dark photon. The collider sensitivity curves at the 90 % C.L. in the mass range of mediators up to several GeV demonstrate the power of the future electron-positron collider for dark matter manifestations' search. A self-consistent dark matter model containing an additional scalar and a massive vector is proposed, and exact terms for the interactions between additional bosons and fermionic fields of the Standard Model are obtained.The limiting case of small mixing and small masses of the dark vector is considered.
11.10.Ef Lagrangian and Hamiltonian approach
12.60.-i Models beyond the standard model
14.80.-j Other particles
$^1$M.V.Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics (SINP MSU)