Cosmic strings appear in many well-motivated extensions to the standard model of particle physics. If they exist, an abundant population of compact objects known as cosmic string loops permeate the Universe at all times, providing a secondary source of density perturbations that are large amplitude and non-gaussian in nature. In general, these loops are not stationary in the rest frame of the dark matter, thus their relative velocities will typically seed both spherical and filamentary overdensities in the matter era. Building upon previous work, we provide an improved framework to compute the complete halo mass function for these string seeded overdensities, valid for any loop velocity distribution. Using this mass function, we also compute the subset of halos capable of undergoing a direct collapse, forming a population of black holes with initial mass 10^4-5 \, M_ at high redshifts. Interestingly, for reasonable values of the string parameters, one can reproduce the abundance of ``Little Red Dots" as inferred by JWST.
Bryce Cyr (Wed,) studied this question.