Measurement phases in the critical Ising model exhibit an enlarged replica symmetry, analogous to the Nishimori phenomenon, that exactly determines the Edwards-Anderson correlator exponent in 2D and near six dimensions.
CriticalO(N)mod- els in6−ϵdimensions
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We revisit the classic $O(N)$ symmetric scalar field theories in $d$ dimensions with interaction $(\phi^i \phi^i)^2$. For $2<d<4$ these theories flow to the Wilson-Fisher fixed points for any $N$. A standard large $N$ Hubbard-Stratonovich approach also indicates that, for $4<d<6$, these theories possess unitary UV fixed points. We propose their alternate description in terms of a theory of $N+1$ massless scalars with the cubic interactions $\sigma \phi^i \phi^i$ and $\sigma^3$. Our one-loop calculation in $6-\epsilon$ dimensions shows that this theory has an IR stable fixed point at real values of the coupling constants for $N>1038$. We show that the $1/N$ expansions of various operator scaling dimensions match the known results for the critical $O(N)$ theory continued to $d=6-\epsilon$. These results suggest that, for sufficiently large $N$, there are 5-dimensional unitary $O(N)$ symmetric interacting CFT's; they should be dual to the Vasiliev higher-spin theory in AdS$_6$ with alternate boundary conditions for the bulk scalar. Using these CFT's we provide a new test of the 5-dimensional $F$-theorem, and also find a new counterexample for the $C_T$ theorem.
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Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
A thermal normal-ordering scheme yields systematic epsilon-expansions for thermal observables in PT-symmetric cubic and quintic O(N) models, agreeing with exact 2D results from minimal models M(2,5) and M(3,8)_D and providing higher-d extrapolations.
Develops a Functorial QFT approach and applies it to analyze the O(N) model in AdS, focusing on crossed-channel diagram contributions to conformal block decomposition in the non-singlet sector.
citing papers explorer
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Bayesian phase transition for the critical Ising model: Enlarged replica symmetry in the epsilon expansion and in 2D
Measurement phases in the critical Ising model exhibit an enlarged replica symmetry, analogous to the Nishimori phenomenon, that exactly determines the Edwards-Anderson correlator exponent in 2D and near six dimensions.
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Local CFTs extremise $F$
Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
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$\mathcal{PT}$-symmetric Field Theories at Finite Temperature
A thermal normal-ordering scheme yields systematic epsilon-expansions for thermal observables in PT-symmetric cubic and quintic O(N) models, agreeing with exact 2D results from minimal models M(2,5) and M(3,8)_D and providing higher-d extrapolations.
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Strongly Coupled Quantum Field Theory in Anti-de Sitter Spacetime
Develops a Functorial QFT approach and applies it to analyze the O(N) model in AdS, focusing on crossed-channel diagram contributions to conformal block decomposition in the non-singlet sector.