M2-branes on M-folds

TL;DR

This work identifies the moduli space of the Bagger-Lambert A_4 theory at level $k$ as $(\mathbb{R}^8 \times \mathbb{R}^8)/D_{2k}$ and proposes that the theory describes two M2-branes on a ${\mathbb Z}_{2k}$ M-fold, unifying M-theory perspectives with 3d SCFT data. The authors show that in the large-$k$ limit the system reduces to D2-branes, consistent with M-theory compactification on a circle and a cylinder-like local geometry; for $k=1$ the setup matches two D2-branes on an $O2^-$ orientifold and the IR is the maximally supersymmetric $SO(4)$ theory. They further argue that the chiral primary spectrum aligns with this brane picture, and discuss a geometric picture involving a 2k-gon quiver whose dihedral symmetry produces the moduli-space quotient. Appendices address the Chern-Simons level quantization for $SO(n)$ and monopole charge quantization, supporting the consistency of the proposed framework. Overall, the paper provides a concrete Lagrangian realization of two M2-branes on a Z_{2k} orbifold and clarifies how M-theory compactification emerges in a controlled field-theoretic setting.

Abstract

We argue that the moduli space for the Bagger-Lambert A_4 theory at level k is (R^8 \times R^8)/D_{2k}, where D_{2k} is the dihedral group of order 4k. We conjecture that the theory describes two M2-branes on a Z_{2k} ``M-fold'', in which a geometrical action of Z_{2k} is combined with an action on the branes. For k=1, this arises as the strong coupling limit of two D2-branes on an O2^- orientifold, whose worldvolume theory is the maximally supersymmetric SO(4) gauge theory. Finally, in an appropriate large-k limit we show that one recovers compactified M-theory and the M2-branes reduce to D2-branes.