AI 中文总结
本文研究AdS$_4$中带Neumann边界条件的量子杨-米尔斯理论，定义自对偶极限并证明其等价于自对偶杨-米尔斯理论的BF形式，给出树级关联函数的相关结果并完成平直空间极限下的约化。
AI 中文摘要
本文研究带有Neumann边界条件的欧氏AdS$_4$中的量子杨-米尔斯理论，其依赖于复耦合常数$\frac{1}{g_\text{}^2} \frac{1}{g^2}\frac{i \theta }{8 \text{}^2}$，定义“自对偶极限”为$g_- \to 0$且$g_+$固定，论证该极限理论在微扰下良定义，等价于自对偶杨-米尔斯理论的BF形式，其边界$\text{AdS}_4$处有联系$B$和$F$的特定边界条件；$g_+$是自对偶理论的圈计数参数，这与平直空间中$\theta$对微扰动力学无影响的情况形成鲜明对比。研究还表明，在自对偶极限下，所有树级零正和单正边界关联函数均消失，给出了任意数量胶子的双正树关联函数的闭式表达式；最后证明，在AdS$_4$的平直空间极限下，树级边界关联函数中的总能量极点可正确约化为单负胶子振幅。
英文摘要
Quantum Yang-Mills theory in Euclidean AdS$_4$ with Neumann boundary conditions is studied as a function of the complex couplings $\frac{1}{g_\pm^2} \equiv \frac{1}{g^2}\mp \frac{i θ}{8 π^2}$. We define a "self-dual limit" by $g_- \to 0$ with $g_+ ~{\rm fixed}$. We argue that the limiting theory is well-defined perturbatively and equivalent to the BF formulation of self-dual Yang-Mills theory with a particular boundary condition relating $B$ and $F$ at the boundary $\partial$AdS$_4$. $g_+$ is the loop-counting parameter of the self-dual theory. This is in stark contrast to flat space, where $θ$ has no effect on perturbative dynamics. In the self-dual limit, it is shown that all tree-level zero-plus and single-plus boundary correlators vanish. A closed form expression is given for any number of gluons for the double-plus tree correlators. Finally, we show that in the flat space limit of AdS$_4$, the total energy poles in the tree boundary correlators correctly reduce to the single-minus gluon amplitudes.
Comments30 pages + 6 appendices, 6 figures
