论文标题
在1/n^4的斜利和扭曲
Tilings and Twist at 1/N^4
论文作者
论文摘要
我们重新考虑操作员在所谓的$ su（2）$ sector中混合$ {\ cal n} \，= \，4 $ super yang-mills理论与量规组$ su（n）$。在可能的情况下，具有中等长度的单个跟踪操作员将通过更高跟踪混合物完成，以产生大型$ N $ Tree级特征。 我们对三种激动的平价对特别感兴趣。由于在混合中尊重奇偶校验，因此低长度的奇数单轨道操作员无法获得太多的混合物。我们通过集成方法重现了一组大型$ n $ eigenstates的树级规范，直至订购$ 1/n^4 $。这涉及评估球体，圆环和双道螺旋的两点函数。只要混合不存在后代，就可以找到完美的匹配。 使用Twist使后代出现在整合性图片中，立即导致了如何修改六边形镶嵌物中发生的纠缠状态的问题。我们仔细研究了均等的双迹径混合物，即使是三个兴奋的操作员，这是主要状态和后代的产物。它们的两点函数对引入伯特方程的扭曲敏感。对于横向标量刺激，我们成功地恢复了相应的场理论结果。对于纵向镁，我们的方法失败了，指出了形式主义的潜在弱点。
We re-consider operator mixing in the so-called $SU(2)$ sector of ${\cal N} \, = \, 4$ super Yang-Mills theory with gauge group $SU(N)$. Where possible, single-trace operators of moderate length are completed by higher-trace admixtures so as to yield large $N$ tree level eigenstates. We are particularly interested in parity pairs with three excitations. Since parity is respected in the mixing, the odd single-trace operators at low length cannot receive too many admixtures. We reproduce the tree-level norms of a set of large $N$ eigenstates up to order $1/N^4$ by integrability methods. This involves evaluating two-point functions on the sphere, the torus, and the double-torus. A perfect match is found as long as descendents are absent from the mixing. Using twist to make the descendents appear in the integrability picture immediately leads to the question how to modify the entangled states occurring in the hexagon tessellations. We take a closer look at the double-trace admixtures to the parity even three-excitation operator at length seven, which are both products of a primary state and a descendent. Their two-point functions are sensitive to the twist introduced into the Bethe equations. For transverse scalar excitations we succeed in recovering the corresponding field theory results. For longitudinal magnons our methods fail, pointing at a potential weakness of the formalism.
