An M2/M5 Duality from the Giant Graviton Expansion

TL;DR

We propose a precise M2/M5 duality for BPS indices using the giant graviton expansion, relating the M5 index $\\mathcal{I}_{\\text{M5}}$ to a residue of the M2 grand canonical index $\\Xi_{\\text{M2}}(\\mu;\\tilde{\\omega};\\tilde{\\Delta}_A)$ at $\\Lambda=e^{-\\Delta_2 N}$, with a universal factor $\\mathcal{I}_{\\infty}$ and a linear constraint $\\Delta_1+\\Delta_2-\\omega_1-\\omega_2-\\omega_3=2\\pi i$. The authors validate this relation in the Higgs branch and in the six-dimensional Cardy regime, showing that leading large-$N$ terms reproduce the thermal anomaly polynomial of the 6d theory and that subleading Cardy terms align with known results, while predicting higher-order corrections from the M2 side. They also connect the Cardy expansion of the M5 index to the equivariant integral of the thermal anomaly polynomial $P_8^T$, strengthening the link between 6d anomalies and 3d/4d holographic data. The work opens avenues to extend the duality to other levels $k$, relate to $S^3_b$ partition functions, and explore holographic interpretations of higher-derivative corrections in AdS backgrounds.

Abstract

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.