Exact effective action for the O(N) vector model in the large N limit

TL;DR

This paper derives an exact Wilsonian effective action for the critical O(N) vector model at large N, revealing the detailed RG flow and operator mappings between UV and IR fixed points.

Contribution

It provides a closed-form, transcendental effective action solution for the large N O(N) model, elucidating the UV-IR operator correspondence.

Findings

Exact effective action expressed as a transcendental function

Mapping between UV and IR operators with infinitely many derivatives

Description of RG flow from UV to IR fixed point

Abstract

We present the Wilsonian effective action as a solution of the exact RG equation for the critical $O(N)$ vector model in the large $N$ limit. Below four dimensions, the exact effective action can be expressed in a closed form as a transcendental function of two leading scaling operators with infinitely many derivatives. From the exact solution that describes the RG flow from a UV theory to the fixed point theory in the IR, we obtain the mapping between UV operators and IR scaling operators. It is shown that IR scaling operators are given by sums of infinitely many UV operators with infinitely many derivatives.