标题： ABJM理论中平方幅度的隐藏排列对称性 显示英文标题

标题： A Hidden Permutation Symmetry of Squared Amplitudes in ABJM Theory

摘要： 我们定义平面Aharony-Bergman-Jafferis-Maldacena理论（ABJM）中的平方振幅，类似于$\mathcal{N}{=}4$超杨-米尔斯理论（SYM）中的情况。 令人惊讶的是，固定$N{:=}n{+}L$的$n$点$L$环积分被统一在一个生成函数中。 类似于SYM四点半BPS关联函数积分，该生成函数在对偶空间中享有隐藏的$S_N$置换对称性，使我们可以将其写成权为3的平面$f$图的线性组合。 值得注意的是，通过Gram恒等式，它也可以表示为双部$f$图的线性组合，这体现了该理论中不存在奇数重振幅的重要性质。 The generating function and these properties are explicitly checked against squared amplitudes for all $n$ with $N{=}4,6,8$. By drawing analogies with SYM, we conjecture some graphical rules the generating function satisfy, and exploit them to bootstrap a unique $N{=}10$ result, which provides new results for $n{=}10$ squared tree amplitudes, as well as integrands for $(n,L){=}(4,6),(6,4)$. Our results strongly suggest the existence of a "bipartite correlator" in ABJM theory that unifies all squared amplitudes and satisfies physical constraints underlying these graphical rules. 显示英文摘要

摘要： We define the square amplitudes in planar Aharony-Bergman-Jafferis-Maldacena theory (ABJM), analogous to that in $\mathcal{N}{=}4$ super-Yang-Mills theory (SYM). Surprisingly, the $n$-point $L$-loop integrands with fixed $N{:=}n{+}L$ are unified in a single generating function. Similar to the SYM four-point half-BPS correlator integrand, the generating function enjoys a hidden $S_N$ permutation symmetry in the dual space, allowing us to write it as a linear combination of weight-3 planar $f$-graphs. Remarkably, through Gram identities it can also be represented as a linear combination of bipartite $f$-graphs which manifest the important property that no odd-multiplicity amplitude exists in the theory. The generating function and these properties are explicitly checked against squared amplitudes for all $n$ with $N{=}4,6,8$. By drawing analogies with SYM, we conjecture some graphical rules the generating function satisfy, and exploit them to bootstrap a unique $N{=}10$ result, which provides new results for $n{=}10$ squared tree amplitudes, as well as integrands for $(n,L){=}(4,6),(6,4)$. Our results strongly suggest the existence of a "bipartite correlator" in ABJM theory that unifies all squared amplitudes and satisfies physical constraints underlying these graphical rules.