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Bounds on multiscalar CFTs in the epsilon expansion
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abstract
We study fixed points with N scalar fields in $4 - \varepsilon$ dimensions to leading order in $\varepsilon$ using a bottom-up approach. We do so by analyzing O(N) invariants of the quartic coupling $\lambda_{ijkl}$ that describes such CFTs. In particular, we show that $\lambda_{iijj}$ and $\lambda_{ijkl}^2$ are restricted to a specific domain, refining a result by Rychkov and Stergiou. We also study averages of one-loop anomalous dimensions of composite operators without gradients. In many cases, we are able to show that the O(N) fixed point maximizes such averages. In the final part of this work, we generalize our results to theories with N complex scalars and to bosonic QED. In particular we show that to leading order in $\varepsilon$, there are no bosonic QED fixed points with N < 183 flavors.
Forward citations
Cited by 2 Pith papers
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Coupled minimal models revisited II: Constraints from permutation symmetry
For coupled large-m minimal models with N=5,6,7, every permutation-charged current below spin 10 acquires an anomalous dimension, so the IR fixed points show no extended chiral algebra in that range.
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Gradient Flows and the Curvature of Theory Space
The space of multiscalar field theories carries a curved metric determined by gradient flow, and the gradient-flow potential and metric can be matched to F-tilde and the Zamolodchikov metric at fixed points.
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