Apparently non-invariant terms of nonlinear sigma models in lattice perturbation theory

Abstract

Apparently non-invariant terms (ANTs) which appear in loop diagrams for nonlinear sigma models (NLSs) are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to "pion" fields, we employ lattice regularization, in which everything (including the Jacobian) is well-defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the "pion" fields at one-loop and the Jacobian does not play an important role in generating ANTs.

17 pages, 5 figures

References in corpus (5)

• A Weak Power-Counting Theorem for the Renormalization of the Non-Linear Sigma Model in Four Dimensions
• Endowing the Nonlinear Sigma Model with a Flat Connection Structure: a Way to Renormalization
• Chiral Pertubation Theory with lattice regularization
• Renormalization of the Non-Linear Sigma Model in Four Dimensions. A two-loop example
• Further Comments on the Symmetric Subtraction of the Nonlinear Sigma Model

Cited by in corpus (3)

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• Wilsonian renormalization group analysis of nonrelativistic three-body systems without introducing dimerons