Higher-order asymptotics and critical indexes in the ϕ³ theory

Instanton analysis is applied to the scalar ϕ³ theory. Higher-order asymptotic expansions of the renormalization constants in the minimal subtraction scheme and 6−ϵ dimensional regularization and of the index η are found. Results of the Borel resummation for the presently known terms of the ϵ-expansion of the index η up to the order ϵ⁴ are presented