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arXiv · 2003.02773

Wilson Action for the $O(N)$ Model

Semanti Dutta·B. Sathiapalan·H. Sonoda
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Abstract

In this paper the fixed-point Wilson action for the critical $O(N)$ model in $D=4-\eps$ dimensions is written down in the $\eps$ expansion to order $\eps^2$. It is obtained by solving the fixed-point Polchinski Exact Renormalization Group equation (with anomalous dimension) in powers of $\eps$. This is an example of a theory that has scale and conformal invariance despite having a finite UV cutoff. The energy-momentum tensor for this theory is also constructed (at zero momentum) to order $\eps^2$. This is done by solving the Ward-Takahashi identity for the fixed point action. It is verified that the trace of the energy-momentum tensor is proportional to the violation of scale invariance as given by the exact RG, i.e., the $\beta$ function. The vanishing of the trace at the fixed point ensures conformal invariance. Some examples of calculations of correlation functions are also given.

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Semanti Dutta, B. Sathiapalan, H. Sonoda. 2020-03-05. Wilson Action for the $O(N)$ Model. https://doi.org/10.1016/j.nuclphysb.2020.115022

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