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

Han Ma, Sung-Sik Lee

SciPost Phys. 15, 111 (2023) · published 22 September 2023

- doi: 10.21468/SciPostPhys.15.3.111
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### 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.

### Authors / Affiliations: mappings to Contributors and Organizations

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^{1}Han Ma, -
^{1}^{2}Sung-Sik Lee

^{1}Perimeter Institute [PI]^{2}McMaster University

Funders for the research work leading to this publication