Stability analysis of a non-unitary CFT

DOI10.1007/JHEP11(2023)042arXiv2203.08843OpenAlexW4388536888MaRDI QIDQ6142614

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Publication date: 26 January 2024

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Abstract: We study instability of the lowest dimension operator (it i.e., m the imaginary part of its operator dimension) in the rank-$Q$ traceless symmetric representation of the $O(N)$ Wilson-Fisher fixed point in $D=4+epsilon$. We find a new semi-classical bounce solution, which gives an imaginary part to the operator dimension of order $Oleft(epsilo{n}^{-1/2}expleft[-fracN+83epsilonF(epsilonQ)ight]ight)$ in the double-scaling limit where $epsilonQleqfracN+86sqrt3$ is fixed. The form of $F(epsilonQ)$, normalised as $F(0)=1$, is also computed. This non-perturbative correction continues to give the leading effect even when $Q$ is finite, indicating the instability of operators for any values of $Q$. We also observe a phase transition at $epsilonQ=fracN+86sqrt3$ associated with the condensation of bounces, similar to the Gross-Witten-Wadia transition.

Full work available at URL: https://arxiv.org/abs/2203.08843

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