论文标题
$ \ Mathbf {\ Mathcal n = 2} $ SuperCongron -grongral Theories和Bessel内核中的强耦合扩展
Strong coupling expansion in $\mathbf{\mathcal N=2}$ superconformal theories and the Bessel kernel
论文作者
论文摘要
我们认为在特殊的四维$ \ MATHCAL n = 2 $的超级符合模型中，与$ \ Mathcal n = 4 $ Super Yang-Mills理论相等的超级符合模型。这些模型中的各种可观察物可以在贝塞尔操作员的弗雷德尔姆决定因素方面以$ n $大致表达本地化矩阵模型表示。后者先前出现在矩阵模型中的水平间距分布的研究中，最近在平面$ \ mathcal n = 4 $ sym中无限沉重的半bps运算符的四点相关函数中。我们使用这种关系和适当的广义szego-akhiezer-kac公式来得出领先的校正对自由能的强大耦合扩展，半bps圆形的威尔逊循环以及$ \ Mathcal n = 2 $型号中的手西里尔初选运营商的某些相关器。这在文献中大大概括了部分结果，并代表了ADS/CFT上下文中的双弦理论计算的挑战。我们还证明，由此产生的强耦合膨胀遭受了骨质奇异性的影响，并且需要添加非扰动的，指数抑制的校正。作为我们分析的副产品，我们确定了对上述四点相关器的非扰动校正，以平面$ \ Mathcal n = 4 $ Sym。
We consider strong 't Hooft coupling expansion in special four-dimensional $\mathcal N=2$ superconformal models that are planar-equivalent to $\mathcal N=4$ super Yang-Mills theory. Various observables in these models that admit localization matrix model representation can be expressed at large $N$ in terms of a Fredholm determinant of a Bessel operator. The latter previously appeared in the study of level spacing distributions in matrix models and, more recently, in four-point correlation functions of infinitely heavy half-BPS operators in planar $\mathcal N=4$ SYM. We use this relation and a suitably generalized Szego-Akhiezer-Kac formula to derive the strong 't Hooft coupling expansion of the leading corrections to free energy, half-BPS circular Wilson loop, and certain correlators of chiral primaries operators in the $\mathcal N=2$ models. This substantially generalizes partial results in the literature and represents a challenge for dual string theory calculations in AdS/CFT context. We also demonstrate that the resulting strong-coupling expansions suffer from Borel singularities and require adding non-perturbative, exponentially suppressed corrections. As a byproduct of our analysis, we determine the non-perturbative correction to the above mentioned four-point correlator in planar $\mathcal N=4$ SYM.
