Following the flow for large N and large charge

TL;DR

This paper explores the O(2N) vector model in three dimensions using a double-scaling limit of large N and charge, enabling analysis of the RG flow from UV to IR without complex Feynman diagram calculations.

Contribution

It introduces a method to study the model away from the critical point by relating the effective potential to the Legendre transform of the grand potential at fixed charge.

Findings

Effective potential is the Legendre transform of the grand potential.

Allows simple computation of the effective action and free energy.

Enables analysis of RG flow without Feynman diagrams.

Abstract

We discuss the O(2N) vector model in three dimensions. While this model flows to the Wilson-Fisher fixed point when fine tuned, working in a double-scaling limit of large N and large charge allows us to study the model away from the critical point and even to follow the RG flow from the UV to the IR. The crucial observation is that the effective potential -- at leading order in N but exact to all orders in perturbation theory -- is the Legendre transform of the grand potential at fixed charge. This allows us to write an effective action and the free energy for generic values of the coupling in a very simple fashion and without evaluating any Feynman diagrams.