论文标题
$ n $ n $ - 点相关器的紫外线渐近学 - $ 2 $ su（$ n $）yang-mills理论
UV asymptotics of $n$-point correlators of twist-$2$ operators in SU($N$) Yang-Mills theory
论文作者
论文摘要
生成功能$ \ MATHCAL {W} [J _ {\ MATHCAL O}] $ euclidean相关器twist-$ 2 $ su（$ n $）yang-mills理论承认，' O}] = \ Mathcal {W} _ {sphere} \，\，\，\，[J _ {\ Mathcal O}]+ \ Mathcal {w} _ {w} _ {torus} \，\，\，\，\，\，\，[非扰动，$ \ Mathcal {w} _ {sphere} \，\，\，\，[j _ {j _ {\ Mathcal o}] $是涉及粘合球传播器和顶点的树图的总和，而$ \ \ \ \ \ \ \ \ \ \ \ {w} _ _ {w} _ { o}] $是粘合一环图的总和。此外，已经预测，$ \ Mathcal {w} _ {torus} \，\，\，[j _ {j _ {\ Mathcal O}] $应接纳功能确定性求和胶合球一圈一循环一循环一圈图的对数的结构。我们以封闭形式的ultraviolet（UV）渐近•$ \ Mathcal {w} _ {sphere} \，\，\，\，[J _ {\ Mathcal O}，λ] \ sim \ Mathcal \ Mathcal {w} _ {Asym \，Asym \，Asym \，Asym \，Asym \，Asym \，Asym \，Sphere} _ {j _ {j _ {j _ {莎\，\，\，\，\，\，[j _ {\ Mathcal o}，λ] $在坐标表示中，因为相关器的所有坐标都由因子$λ\ rightarrow 0 $ 0 $均匀地重新缩放。值得注意的是，我们验证了上述预测，即$ \ MATHCAL {w} _ {asym \，torus} \，\，\，\，\，\，\，\，[j _ {j _ {\ Mathcal o}，λ] $ - 在uv to uv to $ \ mathcal中是偶然的\，\，\，[j _ {\ Mathcal O}，λ] $ - 也接受功能决定因素的对数的结构。因此，上面的计算将大型$ n $ ym理论的非扰动解决方案设置为强紫外线渐近约束，这可能是搜索这种解决方案的关键指南。
The generating functional $\mathcal{W}[J_{\mathcal O}]$ of Euclidean correlators of twist-$2$ operators in SU($N$) Yang-Mills theory admits the 't Hooft large-$N$ expansion: $\mathcal{W}[J_{\mathcal O}]=\mathcal{W}_{sphere}\,\,\,\,[J_{\mathcal O}]+\mathcal{W}_{torus} \,\,\,[J_{\mathcal O}]+ \cdots$. Nonperturbatively, $\mathcal{W}_{sphere} \,\,\,\,[J_{\mathcal O}]$ is a sum of tree diagrams involving glueball propagators and vertices, while $\mathcal{W}_{torus} \,\,\,[J_{\mathcal O}]$ is a sum of glueball one-loop diagrams. Moreover, it has been predicted that $\mathcal{W}_{torus } \,\,\,[J_{\mathcal O}]$ should admit the structure of the logarithm of a functional determinant summing glueball one-loop diagrams. We work out in a closed form the ultraviolet (UV) asymptotics of $\mathcal{W}_{sphere} \,\,\,\,[J_{\mathcal O},λ] \sim \mathcal{W}_{asym \, sphere} \,\,\,\,\,\,\,[J_{\mathcal O},λ]$ and $\mathcal{W}_{torus} \,\,\,[J_{\mathcal O},λ] \sim \mathcal{W}_{asym \, torus} \,\,\,\,\,\,[J_{\mathcal O},λ]$ in the coordinate representation as all the coordinates of the correlators are uniformly rescaled by a factor $λ\rightarrow 0$. Remarkably, we verify the above prediction that $\mathcal{W}_{asym \, torus} \,\,\,\,\,\,[J_{\mathcal O},λ]$ -- being asymptotic in the UV to $\mathcal{W}_{torus} \,\,\,[J_{\mathcal O}, λ]$ -- admits the structure of the logarithm of a functional determinant as well. Hence, the computation above sets strong UV asymptotic constraints on the nonperturbative solution of large-$N$ YM theory and it may be a pivotal guide for the search of such a solution.
