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

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, $c_{3\mathrm{/}2}$ and $c_{1\mathrm{/}2}$, when the sum $j_L+j_R$ is much larger than the difference $\mathrm{\mid }{j}_L-j_R\mathrm{\mid }$. 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 $c_{3\mathrm{/}2}=1.068(4)$ and $c_{1\mathrm{/}2}=0.083(3)$.