Bounds on multiscalar CFTs in the epsilon expansion

TL;DR

This paper analyzes fixed points of multiscalar conformal field theories in four minus epsilon dimensions, refining bounds on couplings, studying anomalous dimensions, and extending results to complex scalars and bosonic QED.

Contribution

It provides new bounds on O(N) invariants, shows the maximization of anomalous dimension averages at fixed points, and extends the analysis to complex scalars and bosonic QED.

Findings

Refined bounds on quartic couplings in multiscalar CFTs.

Fixed points maximize certain anomalous dimension averages.

No bosonic QED fixed points with fewer than 183 flavors at leading order.

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.