The three-loop divergent structure of the two-dimensional non-linear sigma model is computed in a coordinate-space cutoff scheme, including the new countervertices and the squared-logarithm part of the renormalization constant.
Three-loop renormalization of the quantum action for a five-dimensional scalar cubic model with the usage of the background field method and a cutoff regularization
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abstract
The paper studies the quantum action for the five-dimensional real $\phi^3$-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 explicit form of the first three coefficients for the renormalization constants is presented. The absence of non-local singular contributions and partial results for the fourth correction are discussed.
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Three-loop singularity structure for a non-linear sigma model
The three-loop divergent structure of the two-dimensional non-linear sigma model is computed in a coordinate-space cutoff scheme, including the new countervertices and the squared-logarithm part of the renormalization constant.