Calculation of critical index $\eta$ of the ${\phi }^3$-theory in 4-loop approximation by the conformal bootstrap technique

The method of calculation of $\epsilon$-expansion in model of scalar field with ${\phi }^3$-interaction based on conformal bootstrap equations is proposed. This technique is based on self-consistent skeleton equations involving full propagator and full triple vertex. Analytical computations of the Fisher’s index $\eta$ are performed in four-loop approximation. The three-loop result coincides with one obtained previously by the renormalization group equations technique based on calculation of a larger number of Feynman diagrams. The four-loop result agrees with its numerical value obtained by other authors.