论文标题
在$ \ mathcal {n} = 4 $ sym＆supergravity中以$ sl（2，\ mathbb {z}）$ - 平均字符串，以$ \ mathcal {n} = 4 $ sym＆supergravity中的利用s二元性 -
Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings
论文作者
论文摘要
我们开发了一种新方法来提取四维$ \ MATHCAL {n} = 4 $ SUPER YANG-MILLS（SYM）及其字符串理论双重性的S偶尔的物理后果，基于$ SL（2，\ Mathbb {Z}）$ Spectral Theordion。我们观察到，CFT可观察到$ \ Mathcal {O} $，在$ sl（2，\ Mathbb {z}）下不变，将复杂的量规耦合$τ$转换，承认独特的频谱分解为方形函数的基础。该公式对$ \ MATHCAL {n} = 4 $ sym Data的分析结构有直接影响，无论是扰动和非扰动而在所有参数中。例如，$ k $ - instanton部门由零和一个in-instanton部门唯一确定，而Borel impable则围绕$ K $ -Instantons的bore-sumper serivers具有与简单的$ k $依赖性的收敛radii。在很大的$ n $限制中，我们得出了非扰动效果的存在和缩放，我们为某些$ \ nathcal {n} = 4 $ SYM可观察到了这些效果。这些技术的优雅基准是由[arxiv：2102.09537]确定的集成四点函数，用于$ su（n）$ gauge group的所有$τ$；我们得出并阐明其形式。 这些结果对全息图产生了影响。我们解释了$ \ langle \ Mathcal {o} \ rangle $，$ \ Mathcal {n} = 4 $ supersymmetric suppersymmetric conformal歧管相对于Zamolodchikov测量的平均值是由频谱分解干净隔离的。我们证明，$ \ langle \ Mathcal {o} \ rangle $的大$ n $限制等于大$ n $，大't Hooft耦合极限为$ \ MATHCAL {O} $。从图上说，$ \ langle \ Mathcal {o} \ rangle = \ Mathcal {o} _ {\ rm sugra} $，其在ADS $ _5 \ times $ s $ s $ s $^5 $的IIB superGravity中的价值。该结果将其扩展到所有订单$ 1/n $，将合奏嵌入了传统的广告/CFT范式中。 $ sl（2，\ mathbb {z}）$合奏的统计数据表现出扰动和非扰动$ 1/n $效果。
We develop a new approach to extracting the physical consequences of S-duality of four-dimensional $\mathcal{N}=4$ super Yang-Mills (SYM) and its string theory dual, based on $SL(2,\mathbb{Z})$ spectral theory. We observe that CFT observables $\mathcal{O}$, invariant under $SL(2,\mathbb{Z})$ transformations of a complexified gauge coupling $τ$, admit a unique spectral decomposition into a basis of square-integrable functions. This formulation has direct implications for the analytic structure of $\mathcal{N}=4$ SYM data, both perturbatively and non-perturbatively in all parameters. For example, $k$-instanton sectors are uniquely determined by the zero- and one-instanton sectors, and Borel summable series around $k$-instantons have convergence radii with simple $k$-dependence. In large $N$ limits, we derive the existence and scaling of non-perturbative effects, which we exhibit for certain $\mathcal{N}=4$ SYM observables. An elegant benchmark for these techniques is the integrated four-point function conjecturally determined by [arXiv:2102.09537] for all $τ$ for $SU(N)$ gauge group; we derive and elucidate its form. These results have ramifications for holography. We explain how $\langle\mathcal{O}\rangle$, the ensemble average over the $\mathcal{N}=4$ supersymmetric conformal manifold with respect to the Zamolodchikov measure, is cleanly isolated by the spectral decomposition. We prove that the large $N$ limit of $\langle\mathcal{O}\rangle$ equals the large $N$, large 't Hooft coupling limit of $\mathcal{O}$. Holographically speaking, $\langle\mathcal{O}\rangle = \mathcal{O}_{\rm sugra}$, its value in type IIB supergravity on AdS$_5 \times$ S$^5$. This result, which extends to all orders in $1/N$, embeds ensemble averaging into the traditional AdS/CFT paradigm. The statistics of the $SL(2,\mathbb{Z})$ ensemble exhibit both perturbative and non-perturbative $1/N$ effects.
