# Conformal dimensions in the large charge sectors at the O(4) Wilson-Fisher fixed point

## TL;DR

This paper derives a formula for conformal dimensions in large-charge sectors of the 3D O(4) model, validated by Monte Carlo simulations, providing new insights into operator scaling at the Wilson-Fisher fixed point.

## Contribution

It introduces an effective field theory formula for conformal dimensions in large-charge sectors and confirms it with Monte Carlo calculations, estimating key constants.

## Key findings

- Derived a formula for conformal dimensions $D(j_L, j_R)$ in large-charge sectors.
- Validated the formula with Monte Carlo simulations for $j_L = j_R$, showing excellent agreement.
- Estimated constants $c_{3/2}=1.068(4)$ and $c_{1/2}=0.083(3)$ from numerical data.

## Abstract

We study the O(4) Wilson-Fisher fixed point in 2+1 dimensions in fixed large-charge sectors identified by products of two spin-j representations $(j_L, j_R)$. Using effective field theory we derive a formula for the conformal dimensions $D(j_L, j_R)$ of the leading operator in terms of two constants, $c_{3/2}$ and $c_{1/2}$, when the sum $j_L + j_R$ is much larger than the difference $|j_L-j_R|$. We compute $D(j_L,j_R)$ when $j_L = j_R$ with Monte Carlo calculations in a discrete formulation of the O(4) lattice field theory, and show excellent agreement with the predicted formula and estimate $c_{3/2}=1.068(4)$ and $c_{1/2}=0.083(3)$.