  We perform a bootstrap analysis of a mixed system of four-point functions of
bosonic and fermionic operators in parity-preserving 3d CFTs with O(N) global
symmetry. Our results provide rigorous bounds on the scaling dimensions of the
O(N)-symmetric Gross-Neveu-Yukawa (GNY) fixed points, constraining these
theories to live in isolated islands in the space of CFT data. We focus on the
cases N = 1, 2, 4, 8, which have applications to phase transitions in condensed
matter systems, and compare our bounds to previous analytical and numerical
results.
