Hidden Permutation Symmetry of Squared Amplitudes in Aharony-Bergman-Jafferis-Maldacena Theory

We define the "squared amplitudes" in planar Aharony-Bergman-Jafferis-Maldacena theory, analogous to those in N=4 super-Yang-Mills (SYM) theory. 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-Bogomol'nyi-Prasad-Sommerfield 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 that 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 satisfies, 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 Aharony-Bergman-Jafferis-Maldacena theory that unifies all squared amplitudes and satisfies physical constraints underlying these graphical rules.