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

4+4 pages, 6 figures

References in corpus (4)

• The large-charge expansion for Schrödinger systems
• Matrix models at large charge
• Modeling pion physics in the $\epsilon$-regime of two-flavor QCD using strong coupling lattice QED
• Anomaly and a QCD-like phase diagram with massive bosonic baryons

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