论文标题
$ \ MATHCAL {n} = 4 $ SUPER YANG-MILLS中的引导混合相关器
Bootstrapping mixed correlators in $\mathcal{N}=4$ Super Yang-Mills
论文作者
论文摘要
我们对混合相关系统进行了数值自举研究，该系统包含二维和三个的半bps操作员，$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ h = 4 $ super yang-mills。这种设置改进了文献中仅考虑一个或另一个操作员的单个相关器的先前作品。通过在所有操作员的扭曲上施加差距而不是单个尺寸，我们在R-对称的给定表示中获得了上限的上限。结果，我们发现大型$ n $超级预测与数值有限$ n $结果之间的张力已经达到$ n \ sim 100 $。讨论了一些可能的解决方案：极好的频谱表明，除了双重痕量运营商外，在整个但有限的$ n $之外，还有一个具有较小尺寸的国家塔。我们还获得了有关运算符维度的新界限，而单个相关器设置无法访问。最后，我们考虑了各种操作员的OPE系数的界限。最轻的标量单线的OPE系数获得的结果显示了二维形成式歧管的证据。
We perform a numerical bootstrap study of the mixed correlator system containing the half-BPS operators of dimension two and three in $\mathcal N = 4$ Super Yang-Mills. This setup improves on previous works in the literature that only considered single correlators of one or the other operator. We obtain upper bounds on the leading twist in a given representation of the R-symmetry by imposing gaps on the twist of all operators rather than the dimension of a single one. As a result we find a tension between the large $N$ supergravity predictions and the numerical finite $N$ results already at $N\sim 100$. A few possible solutions are discussed: the extremal spectrum suggests that at large but finite $N$, in addition to the double trace operators, there exists a second tower of states with smaller dimension. We also obtain new bounds on the dimension of operators which were not accessible with a single correlator setup. Finally we consider bounds on the OPE coefficients of various operators. The results obtained for the OPE coefficient of the lightest scalar singlet show evidences of a two dimensional conformal manifold.
