Wilson Action for the $O(N)$ Model

Understand

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 $\eps^2$.