For semisimple Lie algebra targets
For discrete group targets
For discrete 2-group targets
For Lie 2-algebra targets
For targets extending the super Poincare Lie algebra
(such as the supergravity Lie 3-algebra, the supergravity Lie 6-algebra)
Chern-Simons-supergravity
for higher abelian targets
for symplectic Lie n-algebroid targets
for the $L_\infty$-structure on the BRST complex of the closed string:
higher dimensional Chern-Simons theory
topological AdS7/CFT6-sector
The ABJM model (ABJM 08) is 3-dimensional $\mathcal{N} = 6$ supersymmetric Chern-Simons theory with gauge group SU(N) and coupled to matter fields. For Chern-Simons level $k$ it is supposed to describe the worldvolume theory of $N$ coincident black M2-branes at an $\mathbb{Z}/k$-cyclic group orbifold singularity with near-horizon geometry $AdS_4 \times S^7/(\mathbb{Z}/k)$ (see at M2-branes – As a black brane).
For $k = 2$ the supersymmetry of the ABJM model increases to $\mathcal{N} = 8$. For $k = 2$ and $N = 2$ the ABJM model reduces to the BLG model (ABJM 08, section 2.6).
Due to the matter coupling, the ABJM model is no longer a topological field theory as pure Chern-Simons is, but it is still a conformal field theory. As such it is thought to correspond under AdS-CFT duality to M-theory on AdS4 $\times$ S7/$\mathbb{Z}/k$ (see also MFFGME 09).
Notice that the worldvolume $SU(N)$ gauge group enhancement at an $\mathbb{Z}_k$-ADE singularity is akin to the gauge symmetry enhancement of the effective field theory for M-theory on G2-manifolds at the same kind of singularities (see at M-theory on G2-manifolds – Nonabelian gauge groups).
Under holographic duality supposed to be related to M-theory on $AdS_4 \times S^7 / \mathbb{Z}_k$.
Table of branes appearing in supergravity/string theory (for classification see at brane scan).
The original article is
Discussion of extension to boundary field theory (describing M2-branes ending on M5-branes) includes
A kind of double dimensional reduction of the ABJM model to something related to type II superstrings and D1-branes is discussed in
Discussion of the ABJM model in Horava-Witten theory and reducing to heterotic strings is in
Discussion of the model as a higher gauge theory (due to its coupling to the supergravity C-field) is in
Sam Palmer, Christian Saemann, section 2 of M-brane Models from Non-Abelian Gerbes, JHEP 1207:010, 2012 (arXiv:1203.5757)
Sam Palmer, Christian Saemann, The ABJM Model is a Higher Gauge Theory, IJGMMP 11 (2014) 1450075 (arXiv:1311.1997)
Classification of the possible superpotentials? via representation theory is due to
and derived from this a classification of the possble orbifolding is in
Paul de Medeiros, José Figueroa-O'Farrill, Sunil Gadhia, Elena Méndez-Escobar, Half-BPS quotients in M-theory: ADE with a twist, JHEP 0910:038,2009 (arXiv:0909.0163, pdf slides)
Paul de Medeiros, José Figueroa-O'Farrill, Half-BPS M2-brane orbifolds, Adv. Theor. Math. Phys. Volume 16, Number 5 (2012), 1349-1408. (arXiv:1007.4761, Euclid)
José Figueroa-O'Farrill, M2-branes, ADE and Lie superalgebras, talk at IPMU 2009 (pdf)
See also