ABJM
ABJM theory, named after Aharony, Bergman, Jafferis, and Maldacena, is a three-dimensional N=6 superconformal Chern-Simons-matter theory proposed in 2008. It describes the low-energy dynamics of N coincident M2-branes on a C^4/Z_k singularity and is characterized by the gauge group U(N)_k × U(N)_{-k}, with Chern-Simons levels k and −k. The matter content consists of four complex scalar fields and their fermionic superpartners, arranged in bifundamental representations under the two gauge groups. The theory possesses conformal invariance and an SU(4) R-symmetry, together forming the superconformal algebra OSp(6|4). For k=1 or 2, supersymmetry enhances to N=8 and the R-symmetry to SO(8).
Classically, the Lagrangian contains Chern-Simons terms, kinetic terms for matter, and a sextic scalar potential that
ABJM provides a concrete realization of AdS4/CFT3: in the large-N limit with k fixed, the dual description
The theory is integrable in the planar limit and has been extensively studied using localization and other