Bounds on multiscalar CFTs in the epsilon expansion

Abstract

We study fixed points with N scalar fields in $4-\epsilon$ dimensions to leading order in $\epsilon$ 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 $\epsilon$, there are no bosonic QED fixed points with N < 183 flavors.

29 pages + appendices, 10 figures. v2: misprints corrected; v3: added comparison between complex and real bounds, minor edits, version to appear in JHEP

References in corpus (6)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Central Charge Bounds in 4D Conformal Field Theory
• Thermal Order in Conformal Theories
• Easy-plane QED${}_3$'s in the large $N_f$ limit
• On critical models with $N\le 4$ scalars in $d=4-\epsilon$
• Multi-critical multi-field models: a CFT approach to the leading order

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