发表机构
Budapest University of Technology and Economics; HUN-REN Wigner Research Centre for Physics（布达佩斯技术与经济大学; 匈牙利研究网络维格纳物理研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究\(\mathcal{N}=4\)超对称杨-米尔斯理论尖点反常维度及\(\mathrm{O}(6)\)西格玛模型质量间隙在强耦合下的跨级数结构，通过引入倾斜质量间隙等方法确定其强耦合结构，构建外星微积分并推导相关精确关系。
AI 中文摘要
我们研究了\(\mathcal{N}=4\)超对称杨-米尔斯理论的尖点反常维度以及\(\mathrm{O}(6)\)西格玛模型在强\('t\)胡夫特耦合下动态生成的质量间隙的跨级数结构。考虑了尖点反常维度的单参数变形即倾斜尖点，回顾了通过其用具有矩阵贝塞尔核的弗雷德霍姆行列式表示得到的强耦合展开。引入倾斜质量间隙，它在变形参数的特殊值下简化为物理\(\mathrm{O}(6)\)质量间隙，并与倾斜尖点有深刻联系。此公式能确定\(\mathrm{O}(6)\)质量间隙的完整强耦合跨级数和复苏结构，扩展并证明了连续非微扰修正之间的推测关系。基于弗雷德霍姆行列式表示构建了一个外星微积分，可直接从微扰展开生成这些AdS/CFT可观测量的所有非微扰扇区。最后，推导了\(\mathrm{O}(6)\)质量间隙的强耦合跨级数与平面\(\mathcal{N}=4\)超对称杨-米尔斯理论的尖点反常维度之间的精确全阶关系。
英文摘要
We investigate the trans-series structure of the cusp anomalous dimension of $\mathcal{N}=4$ supersymmetric Yang-Mills theory and the dynamically generated mass gap of the $\mathrm{O}(6)$ sigma model at strong 't Hooft coupling. We consider the one-parameter deformation of the cusp anomalous dimension, known as the tilted cusp, and review its strong-coupling expansion obtained through its representation in terms of Fredholm determinants with a matrix Bessel kernel. The advantage of this deformation is that the non-perturbative scales separate naturally, revealing structures that remain hidden in the physical limit. Motivated by this observation, we introduce the tilted mass gap, which reduces to the physical $\mathrm{O}(6)$ mass gap at a special value of the deformation parameter and exhibits a deep connection with the tilted cusp. This formulation allows us to determine the complete strong-coupling trans-series and resurgence structure of the $\mathrm{O}(6)$ mass gap, while extending and proving conjectured relations between successive non-perturbative corrections. Building on the underlying Fredholm determinant representation, we construct an Alien calculus that generates all non-perturbative sectors of these AdS/CFT observables directly from their perturbative expansions. Finally, we derive an exact all-orders relation between the strong-coupling trans-series of the $\mathrm{O}(6)$ mass gap and the cusp anomalous dimension of planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory.
Comments38 pages; references added
