论文标题
Epsilon扩展中多层CFT的界限
Bounds on multiscalar CFTs in the epsilon expansion
论文作者
论文摘要
我们使用自下而上的方法研究了$ 4- \ varepsilon $尺寸的固定点，以$ \ varepsilon $领先订单。我们通过分析了四分之一的耦合$λ_{ijkl} $的o（n）不变性的O（n）。特别是，我们表明$λ_{iijj} $和$λ_{ijkl}^2 $仅限于特定域，并由Rychkov和Stergiou完善结果。我们还研究没有梯度的复合算子的一环异常维度的平均值。在许多情况下，我们能够证明O（n）固定点可以最大化此类平均值。在这项工作的最后一部分中，我们将结果推广到具有n个复杂标量的理论和玻感QED。特别是，我们表明，要以$ \ varepsilon $领先订单，没有带有n <183口味的Bosonic QED固定点。
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 $λ_{ijkl}$ that describes such CFTs. In particular, we show that $λ_{iijj}$ and $λ_{ijkl}^2$ 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.
