论文标题
限制大小的共形理论
Constraining Conformal Theories in Large Dimensions
论文作者
论文摘要
在本文中，我们分析了单位性和对称对称性在大小上的共形理论上施加的约束。特别是，我们表明，在一个大尺寸$ d $中的统一保串理论中，相同的标量运算符$ ϕ $具有比例尺寸$δ__它们的四点函数，因此$δ_ϕ/d <3/4 $必然是广义自由理论的函数。该结果仅来自交叉对称性和单位性。特别是，我们不施加保守的自旋两个操作员（应力张量）的存在。我们还提出了一个参数，将此结果的适用性扩展到较大的共形尺寸，即$δ_DA/D <1 $。此扩展需要对光运算符光谱的一些合理的假设。总之，这些结果表明，如果在较大维度上存在非平凡的共形理论，不一定具有应力张量，则其相关操作员必须与其余的操作员相关。
In this paper, we analyze the constraints imposed by unitarity and crossing symmetry on conformal theories in large dimensions. In particular, we show that in a unitary conformal theory in large dimension $D$, the four-point function of identical scalar operators $ϕ$ with scaling dimension $Δ_ϕ$ such that $Δ_ϕ/D<3/4$, is necessarily that of the generalized free field theory. This result follows only from crossing symmetry and unitarity. In particular, we do not impose the existence of a conserved spin two operator (stress tensor). We also present an argument to extend the applicability of this result to a larger range of conformal dimensions, namely to $Δ_ϕ/D<1$. This extension requires some reasonable assumptions about the spectrum of light operators. Together, these results suggest that if there is a non-trivial conformal theory in large dimensions, not necessarily having a stress tensor, then its relevant operators must be exponentially weakly coupled with the rest.
