Three-loop renormalization of the quantum action for a four-dimensional scalar model with quartic interaction with the usage of the background field method and a cutoff regularization

Abstract

The paper studies the quantum action for the four-dimensional real ${\varphi }^4$-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization in the coordinate representation. The absence of non-local singular contributions and the correctness of the renormalization $\mathcal{R}$-operation on the example of separate three-loop diagrams are also discussed. The explicit form of the first three coefficients for the renormalization constants and for the $\beta$-function is presented. Consistency with previously known results is shown.

arXiv commentLaTeX, 71 pages, 8 figures. Firstly appeared in Russian, February 6, 2024, see https://www.pdmi.ras.ru/preprint/2024/pr2024.html

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• Heat kernel of non-minimal second-order operators
• Renormalization group for effective field theories: cutoff schemes and universality