The $1/n$ expansion in the Gross–Neveu model: Conformal bootstrap calculation of the index $\eta$ in order $1/n^3$

Using the conformal invariance of the Green's functions for the fields in the Gross–Neveu model in the critical regime that was proved earlier, we now use the conformal-bootstrap method for arbitrary space dimension $d$ to calculate the critical dimension of the master field (index \ifmmode \eta \else $\eta$\fi) in order $1/n^3$ and of the auxiliary field in order $1/n^2$, i. e., to an order higher by one than the previously known results.