An M2/M5 Duality from the Giant Graviton Expansion

We conjecture a precise relation between the superconformal indices of two theories defined in different spacetime dimensions. The first is the three-dimensional ABJM theory describing the worldvolume of parallel M2-branes in M-theory on $\mathbb{R}^{10,1}$. The second is the $\mathcal{N}=(2,0)$ theory in six dimensions which describes the worldvolume of parallel M5-branes in the same background. As we review, the existence of such a duality is closely related to Imamura's proposal for the giant graviton expansion of the three-dimensional index. We check our conjecture against various results for the two indices available in the literature. Using an existing proposal of Hristov for the ABJM superconformal index, we verify our conjecture to the first three orders in an expansion around the six-dimensional Cardy limit.