The pseudo-hermitian scalar model exhibits a line of non-unitary 4D fixed points, massless flows between them, and cyclic RG flows, supported by three-loop beta functions and an all-order conjecture.
Irreversibility of the renormalization group flow in non-unitary quantum field theory
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We show irreversibility of the renormalization group flow in non-unitary but ${\cal PT}$-invariant quantum field theory in two space-time dimensions. In addition to unbroken $\mathcal{PT}$-symmetry and a positive energy spectrum, we assume standard properties of quantum field theory including a local energy-momentum tensor and relativistic invariance. This generalizes Zamolodchikov's $c$-theorem to ${\cal PT}$-symmetric hamiltonians. Our proof follows closely Zamolodchikov's arguments. We show that a function $c_{\mathrm{eff}}(s)$ of the renormalization group parameter $s$ exists which is non-negative and monotonically decreasing along renormalization group flows. Its value at a critical point is the "effective central charge" entering the specific free energy. At least in rational models, this equals $c_{\mathrm{eff}}=c-24\Delta$, where $c$ is the central charge and $\Delta$ is the lowest primary field dimension in the conformal field theory which describes the critical point.
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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.
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
Topological defects constrain the allowed RG flows of N=1 superconformal minimal models, first via a bosonic coset description and then for the full superconformal case.
A two-Higgs-doublet model with SU(2)-based marginal operators produces unavoidable cyclic RG flows, pseudo-unitary behavior below pair-production threshold, and Russian Doll VEVs whose period is fixed by the Koide formula to yield three families.
citing papers explorer
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Non-perturbative renormalization group for pseudo-hermitian scalar fields in 4D
The pseudo-hermitian scalar model exhibits a line of non-unitary 4D fixed points, massless flows between them, and cyclic RG flows, supported by three-loop beta functions and an all-order conjecture.
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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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Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
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Defects in N=1 minimal models and RG flows
Topological defects constrain the allowed RG flows of N=1 superconformal minimal models, first via a bosonic coset description and then for the full superconformal case.
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A rich structure of renormalization group flows for Higgs-like models in 4 dimensions
A two-Higgs-doublet model with SU(2)-based marginal operators produces unavoidable cyclic RG flows, pseudo-unitary behavior below pair-production threshold, and Russian Doll VEVs whose period is fixed by the Koide formula to yield three families.
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