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arXiv · 1105.0483

Realization of Chiral Symmetry in the ERG

Yoshio Echigo·Yuji Igarashi
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Abstract

We discuss within the framework of the ERG how chiral symmetry is realized in a linear $σ$ model. A generalized Ginsparg-Wilson relation is obtained from the Ward-Takahashi identities for the Wilson action assumed to be bilinear in the Dirac fields. We construct a family of its non-perturbative solutions. The family generates the most general solutions to the Ward-Takahashi identities. Some special solutions are discussed. For each solution in this family, chiral symmetry is realized in such a way that a change in the Wilson action under non-linear symmetry transformation is canceled with a change in the functional measure. We discuss that the family of solutions reduces via a field redefinition to a family of the Wilson actions with some composite object of the scalar fields which has a simple transformation property. For this family, chiral symmetry is linearly realized with a continuum analog of the operator extension of $γ_5$ used on the lattice. We also show that there exist some appropriate Dirac fields which obey the standard chiral transformations with $γ_5$ in contrast to the lattice case. Their Yukawa interactions with scalars, however, becomes non-linear.

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Yoshio Echigo, Yuji Igarashi. 2011-05-03. Realization of Chiral Symmetry in the ERG. https://doi.org/10.1143/ptp.125.709

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