arXiv 2202.057842022-02hep-th

具有一般经典规范群的$\mathcal{N}=4$ SYM中对偶协变关联函数的精确结果

Exact results for duality-covariant integrated correlators in $\mathcal{N}=4$ SYM with general classical gauge groups

Daniele Dorigoni, Michael B. Green, Congkao Wen

备注：: 38 pages, v2: minor changes, version accepted for publication in SciPost

摘要：

本文给出了经典规范群下$\mathcal{N}=4$超对称杨-米尔斯（SYM）理论中四个超共形原算符在应力张量多重态中的某些积分关联函数的精确表达式：$G_N$ $= SO(2N)$，$SO(2N+1)$，$USp(2N)$ .这些集成的关联函数表示为二维晶格总和考虑局部配分函数的衍生物，概括的表达$SU(N)$在我们以前的作品。这些表达式在Goddart-Nuyts-Olive对偶下显然是协变的。积分关联函数也可以形式化地表示为具有整指数和有理系数的非全纯Eisenstein级数的无穷和。此外，双曲拉普拉斯算子关于复耦合$τ=θ/(2π) + 4πi /g^2_{_{YM}}$对规范群$G_N$的任何积分相关器的作用使其与具有规范群$G_{N+1}$的关联函数、$G_N$和$G_{N-1}$的线性组合有关。这些“拉普拉斯-差分方程”决定了所有经典规范群的积分关联函数的表达式，对于任意的$N$值，都可以用规范群$SU(2)$的关联函数表示。这些集成的关联函数的扰动扩展的$N$的任何有限值同意从微扰杨-米尔斯量子场论得到的属性，连同各种多瞬子计算，这也表明同意超对称局域化所确定的。大- $N$展开式中的项系数是具有半整数指标的非全纯Eisenstein级数之和，推广了最近的结果，并与$AdS_5\times S^5/\mathbb{Z}_2$背景下的IIB型超弦理论的低能展开式中的低阶项联系起来.

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文