Solutions to sign problems in lattice Yukawa models

We prove that sign problems in the traditional approach to some lattice Yukawa models can be completely solved when the fermions are formulated using fermion bags and the bosons are formulated in the worldline representation. We prove this within the context of two examples of three dimensional models, symmetric under $U_L(1) times U_R(1) times Z_2 ({Parity})$ transformations, one involving staggered fermions and the other involving Wilson fermions. We argue that these models have interesting quantum phase transitions that can now be studied using Monte Carlo methods.