On the structure of the large-$N$ expansion in SU($N$) Yang-Mills theory
On the structure of the large-$N$ expansion in SU($N$) Yang-Mills theory
复制标题
论SU($N$)杨-米尔斯理论中大$N$展开的结构
DOI：
--
复制
发表时间：
2024
期刊：
影响因子：
--
通讯作者：
F. Scardino
中科院分区：
文献类型：
--
作者：
M. Bochicchio;M. Papinutto;F. Scardino
最近，我们计算了SU（$N$）Yang-Mills（YM）理论的大N$展开中单迹扭2 $算子的欧几里德算子的生成泛函的短程渐近性.值得注意的是，它具有函数行列式的对数结构，但符号与胶球自旋统计定理的符号相反。为了解决这个符号难题，我们重新考虑了文献中的证明，即在大-$N$ YM理论的't Hooft拓扑展开中，对生成泛函的前导非平面贡献由$n$-穿孔环面的穿孔之和组成。我们已经发现，对于twist-$2$算子，它包含-除了$n$-穿孔环面-具有$1 \leq p \leq n$收缩和$n-p$穿孔的环面的归一化。一旦考虑到新扇区的存在，对自旋统计定理的违反就消失了。此外，新部门的贡献微不足道的非微扰$S$矩阵，因为-例如-的$n$-捏环面代表非微扰循环的$n$胶球传播没有外部腿。这开辟了一个精确的解决方案，限于新的部门，可能是可解决的感谢消失$S$矩阵的方式。
Recently, we have computed the short-distance asymptotics of the generating functional of Euclidean correlators of single-trace twist-$2$ operators in the large-$N$ expansion of SU($N$) Yang-Mills (YM) theory to the leading-nonplanar order. Remarkably, it has the structure of the logarithm of a functional determinant, but with the sign opposite to the one that would follow from the spin-statistics theorem for the glueballs. In order to solve this sign puzzle, we have reconsidered the proof in the literature that in the 't Hooft topological expansion of large-$N$ YM theory the leading-nonplanar contribution to the generating functional consists of the sum over punctures of $n$-punctured tori. We have discovered that for twist-$2$ operators it contains -- in addition to the $n$-punctured tori -- the normalization of tori with $1 \leq p \leq n$ pinches and $n-p$ punctures. Once the existence of the new sector is taken into account, the violation of the spin-statistics theorem disappears. Moreover, the new sector contributes trivially to the nonperturbative $S$ matrix because -- for example -- the $n$-pinched torus represents nonperturbatively a loop of $n$ glueball propagators with no external leg. This opens the way for an exact solution limited to the new sector that may be solvable thanks to the vanishing $S$ matrix.
曲线模空间：古典和热带
影响因子：
--
作者：
Chan, Melody
通讯作者：
Chan, Melody