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

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 $c_{ 1 / 2}=0.083(3)$.