Application of η-expansion technique to the φ3-theory in arbitrary dimension

Abstract

The [Formula: see text]-theory in the Euclidean space of arbitrary dimension is considered in the present paper. The method of [Formula: see text]-expansion in frames of conformal bootstrap equations is used. As one knows, there is an [Formula: see text]-expansion technique that allows one to calculate the critical exponent in the form of a series in [Formula: see text], the deviation of the space dimension from the logarithmic one. However, the given series in [Formula: see text] is divergent, and it is not possible to extend it analytically to arbitrary dimension. To solve the problem, we propose using the [Formula: see text]-expansion: we construct series in powers of the Fisher’s exponent [Formula: see text] or a parameter [Formula: see text] expressed through the Fisher’s exponent and we obtain some approximate equation for [Formula: see text] or [Formula: see text].