论文标题
最大$ u（1）_y $ -violating $ n $ - 点相关器$ \ mathcal {n} = 4 $ super-yang-mills理论
Maximal $U(1)_Y$-violating $n$-point correlators in $\mathcal{N}=4$ super-Yang-Mills theory
论文作者
论文摘要
本文涉及$ n $ n $ n $ point相关功能的特殊类别，在压力张量超过$ \ Mathcal {n} = 4 $ supersymmetric $ su（n）$ yang-mills理论中。这些是“最大$ u（1）_y $ - 污染”的相关器，这些相关器违反了奖金$ u（1）_y $费用，最高为$ 2（n-4）$单位。我们将证明，这种相关器满足$ sl（2，\ mathbb {z}）$ - 协变递归关系，将$ n $ - 点相关器与$（n-1）$ - 点相关器相关联，以类似于软dilaton关系的方式，该关系与平面空间类型IIB iib iib iib iib suberspertring理论中相应的放大相关。 These recursion relations are used to determine terms in the large-$N$ expansion of $n$-point maximal $U(1)_Y$-violating correlators in the chiral sector, including correlators with four superconformal stress tensor primaries and $(n-4)$ chiral Lagrangian operators, starting from known properties of the $n=4$ case.我们将前三个订单集中在超过超级限制之外的$ 1/n $中。相关因子的梅林表示是梅林变量中的多项式，与$ ADS_5 \ times s^5 $在与$ r^4，D^4r^4 $和$ d^6r $和$ d^6r^4 $相同的订单下的IIB型超跨度理论的较高衍生触点术语相对应。发现这些术语的耦合持续依赖性被认为是由具有holomormormormoric和tholomormormormormormormoric重量$（n-4,4-n）$的非单晶模块化形式描述的，即$ sl（2，\ mathbb {z}）$ - eisenstein系列和某些常规的衍生物。这确定了$ U（1）_y $ - 抗化$ n $零件互动（$ n> 4 $）的许多非领先贡献，用于IIB类型IIB型超过弹片幅度的低能扩展，$ ads_5 \ ads_5 \ times s^5 $。
This paper concerns a special class of $n$-point correlation functions of operators in the stress tensor supermultiplet of $\mathcal{N}=4$ supersymmetric $SU(N)$ Yang-Mills theory. These are "maximal $U(1)_Y$-violating" correlators that violate the bonus $U(1)_Y$ charge by a maximum of $2(n-4)$ units. We will demonstrate that such correlators satisfy $SL(2,\mathbb{Z})$-covariant recursion relations that relate $n$-point correlators to $(n-1)$-point correlators in a manner analogous to the soft dilaton relations that relate the corresponding amplitudes in flat-space type IIB superstring theory. These recursion relations are used to determine terms in the large-$N$ expansion of $n$-point maximal $U(1)_Y$-violating correlators in the chiral sector, including correlators with four superconformal stress tensor primaries and $(n-4)$ chiral Lagrangian operators, starting from known properties of the $n=4$ case. We concentrate on the first three orders in $1/N$ beyond the supergravity limit. The Mellin representations of the correlators are polynomials in Mellin variables, which correspond to higher derivative contact terms in the low-energy expansion of type IIB superstring theory in $AdS_5 \times S^5$ at the same orders as $R^4, d^4R^4$ and $d^6R^4$. The coupling constant dependence of these terms is found to be described by non-holomorphic modular forms with holomorphic and anti-holomorphic weights $(n-4,4-n)$ that are $SL(2, \mathbb{Z})$-covariant derivatives of Eisenstein series and certain generalisations. This determines a number of non-leading contributions to $U(1)_Y$-violating $n$-particle interactions ($n>4$) in the low-energy expansion of type IIB superstring amplitudes in $AdS_5\times S^5$.
