Weyl invariant Jacobi forms along Higgsing trees

A bstract Using topological string techniques, we compute BPS counting functions of 5d gauge theories which descend from 6d superconformal field upon circle compactification. Such are naturally organized in terms nodes Higgsing trees. We demonstrate that the specialization partition function as move crown to root a tree is determined by homomorphisms between rings Weyl invariant Jacobi forms. Our computations made feasible fact symmetry enhancements theory manifest on massless spectrum inherited entire tower particles. In some cases, these have nice relation 1-form associated theory.