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

Abstract

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.

9 pages

References in corpus (1)

• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters

Cited by in corpus (5)

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• Multi-loop techniques for massless Feynman diagram calculations
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• Field-theoretic Analysis of Dynamic Isotropic Percolation: Three-loop Approximation
• $F_4$ symmetric ${\varphi }^3$ theory at four loops