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The $O(N)$ Model in $4<d<6$: Instantons and Complex CFTs
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abstract
We revisit the scalar $O(N)$ model in the dimension range $4<d<6$ and study the effects caused by its metastability. As shown in previous work, this model formally possesses a fixed point where, perturbatively in the $1/N$ expansion, the operator scaling dimensions are real and above the unitarity bound. Here, we further show that these scaling dimensions do acquire small imaginary parts due to the instanton effects. In $d$ dimensions and for large $N$, we find that they are of order $e^{-N f(d)}$, where, remarkably, the function $f(d)$ equals the sphere free energy of a conformal scalar in $d-2$ dimensions. The non-perturbatively small imaginary parts also appear in other observables, such as the sphere free energy and two and three-point function coefficients, and we present some of their calculations. Therefore, at sufficiently large $N$, the $O(N)$ models in $4<d<6$ may be thought of as complex CFTs. When $N$ is large enough for the imaginary parts to be numerically negligible, the five-dimensional $O(N)$ models may be studied using the techniques of numerical bootstrap.
Forward citations
Cited by 4 Pith papers
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Surprises in the Ordinary: $O(N)$ Invariant Surface Defect in the $\epsilon$-expansion
The authors compute defect CFT data to third order in the epsilon expansion and discover approximate 'shadow' relations between surface and bulk scaling dimensions.
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Regge trajectories, detectors, and distributions in the critical ${\rm O}(N)$ model
In the critical O(N) model, renormalizing detector and distribution light-ray operators at leading order in 1/N yields Regge intercepts, the leading-twist splitting function, and a BFKL-type anomalous spin.
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The large $N$ vector model on $S^1\times S^2$
The authors compute the leading finite-size corrections to thermal observables of the large-N critical O(N) model on S^1 x S^2 using a perturbative expansion in beta/r.
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Complex CFTs: Holography and Interfaces
Holographic and CFT constructions of interfaces between complex conjugate CFTs, with a leading-order holographic check of the Im-flip relation and super-transmission signatures of non-unitarity.
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