On the UV completion of the \(\mathrm{O}(N)\) model in \(6-\varepsilon\) dimensions: a stable large-charge sector

DOI10.1007/JHEP09(2020)064zbMATH Open1454.81176arXiv2003.13772MaRDI QIDQ1995094

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Publication date: 18 February 2021

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Abstract: We study large charge sectors in the $O(N)$ model in $6-epsilon$ dimensions. For $4<d<6$, in perturbation theory, the quartic $O(N)$ theory has a UV stable fixed point at large $N$. It was recently argued that this fixed point can be described in terms of an IR fixed point of a cubic $O(N)$ model. By considering a double scaling limit of large charge and weak couplings, we compute two-point and all "extremal" higher-point correlation functions for large charge operators and find a precise equivalence between both pictures. Instanton instabilities are found to be exponentially suppressed at large charge. We also consider correlation function of $U(1)$-invariant meson operators in the $O(2N)supsetU(1)imesSU(N)$ theory, as a first step towards tests of (higher spin) $AdS/CFT$.

Full work available at URL: https://arxiv.org/abs/2003.13772

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