The strong effect of three-center interactions on the formation of superconductivity with $\mathbf{d_{x^2-y^2}}$ symmetry in the $\mathbf{t-J^*}$ model

The effect of three-center interactions on the formation of a superconducting phase with $d_{x^2-y^2}$ symmetry is considered using the diagram technique for Hubbard operators and irreducible Green's functions. It is shown that these interactions lead to a decrease in ${T_c}$ by a factor of several tens.