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arXiv 2004.02909hep-th
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IIB型超引力的${\cal {N}}=4$ SYM理论和DIS的自旋1/2费米子算符

Spin-1/2 fermionic operators of ${\cal {N}}=4$ SYM theory and DIS from type IIB supergravity

David Jorrin, Gustavo Michalski, Martin Schvellinger

摘要:

利用规范/引力对偶性研究了带电轻子与极化自旋为1/2的强子的深度非弹性散射。本文计算了${\cal {N}}=4$ SYM理论中自旋为1/2的费米子算符在平面极限和强耦合下的结构函数。具体地说,我们专注于扭转3运营商,这是一个双重的特定的中微子模式,并给出了领先的贡献强子张量。我们认为Bjorken变量的参数范围内$λ^{-1/2}_{SYM} \ll x < 1$超引力对偶描述举行。从IIB型超引力在五球上的降维出发,导出了两个Reynini模和一个无质量矢量场模的相互作用项。这个矢量场是引力子的某些分量和四种形式的势的线性组合。五球上的角积分导致选择规则的相互作用的动力学上的重要后果。这意味着存在新的条款有助于我们明确计算的结构功能。主要贡献来自泡利项,其次是我们发现的新项的贡献。

英文摘要:

We study deep inelastic scattering (DIS) of charged leptons from polarised spin-1/2 hadrons in terms of the gauge/gravity duality. We calculate the structure functions related to spin-1/2 fermionic operators of ${\cal {N}}=4$ SYM theory in the planar limit and at strong coupling. Specifically, we focus on the twist-3 operator which is dual to a certain dilatino mode and gives the leading contribution to the hadronic tensor. We consider the Bjorken variable within the parametric range $λ^{-1/2}_{SYM} \ll x < 1$ where the supergravity dual description holds. From dimensional reduction of type IIB supergravity on the five-sphere, we derive the interaction terms involving two dilatini and a massless vector field mode. This vector field is a linear combination of certain components of the graviton and the four-form potential. The angular integrals on the five-sphere lead to selection rules for the interactions with important consequences on the dynamics. This implies the existence of new terms contributing to the structure functions that we explicitly calculate. The leading contribution comes from the Pauli term, followed by the contributions from the new terms we found.

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