论文标题
超出了强键的$ \ MATHCAL {n} = 4 $ SYM的平面极限
Far Beyond the Planar Limit in Strongly-Coupled $\mathcal{N}=4$ SYM
论文作者
论文摘要
When the $SU(N)$ ${\cal N} = 4$ super-Yang-Mills (SYM) theory with complexified gauge coupling $τ$ is placed on a round four-sphere and deformed by an ${\cal N} = 2$-preserving mass parameter $m$, its free energy $F(m, τ, \bar τ)$ can be computed exactly using supersymmetric localization.在这项工作中，我们得出了第四个衍生物$ \ partial_m^4 f（m，τ，\barτ）\ big | _ {m = 0} $，在$ \ nathcal {n} = 4 $ sempecy中的集成压力量量量多重函数。然后，我们应用这种确切的关系，以及先前工作中得出的各种其他约束（来自分析性启动$ \partial_τ\ partial _ {\ barτ} \ partial_m^2 f（m，τ，\ barτ，\ barτ）在大的$ n $和大型't Hooft耦合中，$ {\ cal n} = 4 $ sym sym相关器在分离点处的扩展。特别是，我们确定$ {\ cal n} = 4 $ sym相关函数在$ 1/n^8 $中的$ {\ cal n} = 4 $ sym相关函数中的领先大$λ$项。这是超出平面限制的三个订单。
When the $SU(N)$ ${\cal N} = 4$ super-Yang-Mills (SYM) theory with complexified gauge coupling $τ$ is placed on a round four-sphere and deformed by an ${\cal N} = 2$-preserving mass parameter $m$, its free energy $F(m, τ, \bar τ)$ can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative $\partial_m^4 F(m, τ, \bar τ) \big|_{m=0}$ of the sphere free energy and the integrated stress-tensor multiplet four-point function in the $\mathcal{N}=4$ SYM theory. We then apply this exact relation, along with various other constraints derived in previous work (coming from analytic bootstrap, the mixed derivative $\partial_τ\partial_{\bar τ} \partial_m^2 F(m, τ, \bar τ) \big|_{m=0}$, and type IIB superstring theory scattering amplitudes) to determine various perturbative terms in the large $N$ and large 't Hooft coupling $λ$ expansion of the ${\cal N} = 4$ SYM correlator at separated points. In particular, we determine the leading large-$λ$ term in the ${\cal N} = 4$ SYM correlation function at order $1/N^8$. This is three orders beyond the planar limit.
