Apparently noninvariant terms of $U(N)\times U(N)$ nonlinear sigma model in the one-loop approximation

Details Apparently noninvariant terms of $U(N)\times U(N)$ nonlinear sigma model in the one-loop approximation Apparently noninvariant terms of $U(N)\times U(N)$ nonlinear sigma model in the one-loop approximation

2009-07-30

arxiv.org/abs/0907.5260v2

Prog. Theor. Phys. 123 (2010), 475-498

Physics

High Energy Physics

High Energy Physics - Theory

two paragraphs added in Introduction, typos in Eqs. fixed

Scientific paper

10.1143/PTP.123.475

We show how the Apparently Noninvariant Terms (ANTs), which emerge in perturbation theory of nonlinear sigma models, are consistent with the nonlinearly realized symmetry by employing the Ward-Takahashi identity (in the form of an inhomogeneous Zinn-Justin equation). In the literature the discussions on ANTs are confined to the SU(2) case. We generalize them to the U(N) case and demonstrate explicitly at the one-loop level that despite the presence of divergent ANTs in the effective action of the "pions", the symmetry is preserved.

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