Feynman diagrams and the large charge expansion in $3-\varepsilon$ dimensions

TL;DR

This paper extends the semiclassical large charge expansion technique from 4−ε dimensions to 3−ε dimensions for the U(1) model, connecting diagrammatic and conformal superfluid regimes and confirming universal behavior in 3D CFTs.

Contribution

It generalizes the large charge expansion method to 3−ε dimensions, providing a unified framework that interpolates between different regimes in U(1) models.

Findings

Reproduces universal O(n^0) contribution to scaling dimensions in 3D CFTs.

Connects diagrammatic calculations with conformal superfluid regime.

Provides a continuous interpolation between different theoretical approaches.

Abstract

In arXiv:1909.01269 it was shown that the scaling dimension of the lightest charge $n$ operator in the $U(1)$ model at the Wilson-Fisher fixed point in $d=4-\varepsilon$ can be computed semiclassically for arbitrary values of $\lambda n$, where $\lambda$ is the perturbatively small fixed point coupling. Here we generalize this result to the fixed point of the $U(1)$ model in $3-\varepsilon$ dimensions. The result interpolates continuously between diagrammatic calculations and the universal conformal superfluid regime for CFTs at large charge. In particular it reproduces the expectedly universal $O(n^0)$ contribution to the scaling dimension of large charge operators in $3d$ CFTs.