Renormalization of the Non-Linear Sigma Model in Four Dimensions. A two-loop example

Ruggero Ferrari; Andrea Quadri

doi:10.1088/1126-6708/2006/01/003

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Renormalization of the Non-Linear Sigma Model in Four Dimensions. A two-loop example

Ruggero Ferrari·Andrea Quadri

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Abstract

The renormalization procedure of the non-linear SU(2) sigma model in D=4 proposed in hep-th/0504023 and hep-th/0506220 is here tested in a truly non-trivial case where the non-linearity of the functional equation is crucial. The simplest example, where the non-linear term contributes, is given by the two-loop amplitude involving the insertion of two ϕ_0 (the constraint of the non-linear sigma model) and two flat connections. In this case we verify the validity of the renormalization procedure: the recursive subtraction of the pole parts at D=4 yields amplitudes that satisfy the defining functional equation. As a by-product we give a formal proof that in D dimensions (without counterterms) the Feynman rules provide a perturbative symmetric solution.

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Ruggero Ferrari, Andrea Quadri. 2005-11-03. Renormalization of the Non-Linear Sigma Model in Four Dimensions. A two-loop example. https://doi.org/10.1088/1126-6708%2F2006%2F01%2F003

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