I will present and analyze two novel classes of non-relativistic string actions. Non-relativistic string theory usually refers to a particular limit of string theory that results in a non-relativistic spectrum, as I will briefly review from a modern geometrical perspective. However, the worldsheet geometry of such strings is still Lorentzian. Motivated in part by decoupling limits of N=4 SYM, I will introduce two related constructions that lead to novel classes of non-relativistic strings with Galilean and Carrollian structures on the worldsheet, respectively.
Time permitting, I will briefly present their Hamiltonian constraint analysis, and I will comment on their potential relevance for accessing new solvable subsectors of AdS/CFT.
