Conformal bootstrap at large charge

DOI10.1007/JHEP05(2018)043zbMATH Open1391.81166arXiv1710.11161WikidataQ129844602 ScholiaQ129844602MaRDI QIDQ1651089

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Publication date: 11 July 2018

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Abstract: We consider unitary CFTs with continuous global symmetries in $d>2$. We consider a state created by the lightest operator of large charge $Qgg1$ and analyze the correlator of two light charged operators in this state. We assume that the correlator admits a well-defined large $Q$ expansion and, relatedly, that the macroscopic (thermodynamic) limit of the correlator exists. We find that the crossing equations admit a consistent truncation, where only a finite number $N$ of Regge trajectories contribute to the correlator at leading nontrivial order. We classify all such truncated solutions to the crossing. For one Regge trajectory $N=1$, the solution is unique and given by the effective field theory of a Goldstone mode. For two or more Regge trajectories $Ngeq2$, the solutions are encoded in roots of a certain degree $N$ polynomial. Some of the solutions admit a simple weakly coupled EFT description, whereas others do not. In the weakly coupled case, each Regge trajectory corresponds to a field in the effective Lagrangian.

Full work available at URL: https://arxiv.org/abs/1710.11161

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