Renormalization of the Non-Linear Sigma Model in Four Dimensions. A two-loop example
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 \phi_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.
Cite
@article{arxiv.hep-th/0511032,
title = {Renormalization of the Non-Linear Sigma Model in Four Dimensions. A two-loop example},
author = {Ruggero Ferrari and Andrea Quadri},
journal= {arXiv preprint arXiv:hep-th/0511032},
year = {2009}
}
Comments
Latex, 3 figures, 19 pages