论文标题
部分可观测时空混沌系统的无模型预测
Exact results for duality-covariant integrated correlators in $\mathcal{N}=4$ SYM with general classical gauge groups
论文作者
论文摘要
我们为$ \ Mathcal {n} = 4 $ supersymmetric yang-mills（sym）理论的应力张量多重组中的四个超符号主要运算符的某些集成相关器提供了精确表达式，$ g_n $ $ $ = so（2n+1）$，$，$，$，$，$，$ USP（2n）$。这些集成的相关器通过考虑局部分区函数的导数来表示为二维晶格总和，从而概括了我们以前的作品中为$ su（n）$获得的表达式。这些表达显然是在戈达德·纳伊特·奥利维二元性下的协变。集成的相关因子也可以正式写为具有整数指数和合理系数的非晶状艾森斯坦序列的无限总和。此外，双曲线拉普拉斯操作员在复杂耦合$τ=θ /（2π） +4πi /g^2 _ {_ {_ {ym}} $上的任何集成相关器$ g_n $都将其与$ g_ $ g_ $ g_ $ g_}相关联的$ g_n $} $ g_ {n-1} $。这些“ Laplace-Difference方程”确定了所有经典量规组的集成相关器的表达式，以$ n $的任何值在量规组$ su（2）$中的相关器中的任何值。这些集成相关器的扰动扩展对于$ n $的任何有限值都与从扰动阳性的属性量量子理论获得的属性，以及各种多in-Instanton计算，也显示出与超对称性定位确定的属性。在很大程度上，术语的系数是具有半数指数的非形态EISENSTEIN系列的总和，这些总和扩展了最新结果，并在$ ADS_5 \ times S^5/\ Mathbb {Z} Z {z} _2 _2 _2 _2 _2 _2 _2 _2 $ ADS_5 \ type superString Theory中与低阶术语接触。
We present exact expressions for certain integrated correlators of four superconformal primary operators in the stress tensor multiplet of $\mathcal{N}=4$ supersymmetric Yang--Mills (SYM) theory with classical gauge group, $G_N$ $= SO(2N)$, $SO(2N+1)$, $USp(2N)$. These integrated correlators are expressed as two-dimensional lattice sums by considering derivatives of the localised partition functions, generalising the expression obtained for $SU(N)$ in our previous works. These expressions are manifestly covariant under Goddard-Nuyts-Olive duality. The integrated correlators can also be formally written as infinite sums of non-holomorphic Eisenstein series with integer indices and rational coefficients. Furthermore, the action of the hyperbolic Laplace operator with respect to the complex coupling $τ=θ/(2π) + 4πi /g^2_{_{YM}}$ on any integrated correlator for gauge group $G_N$ relates it to a linear combination of correlators with gauge groups $G_{N+1}$, $G_N$ and $G_{N-1}$. These "Laplace-difference equation" determine the expressions of integrated correlators for all classical gauge groups for any value of $N$ in terms of the correlator for the gauge group $SU(2)$. The perturbation expansions of these integrated correlators for any finite value of $N$ agree with properties obtained from perturbative Yang--Mills quantum field theory, together with various multi-instanton calculations which are also shown to agree with those determined by supersymmetric localisation. The coefficients of terms in the large-$N$ expansion are sums of non-holomorphic Eisenstein series with half-integer indices, which extend recent results and make contact with low order terms in the low energy expansion of type IIB superstring theory in an $AdS_5\times S^5/\mathbb{Z}_2$ background.
