ABJM theory


\infty-Chern-Simons theory

∞-Chern-Weil theory

∞-Chern-Simons theory

∞-Wess-Zumino-Witten theory




String theory



The ABJM model (ABJM 08) is 3-dimensional 𝒩=6\mathcal{N} = 6 supersymmetric Chern-Simons theory with gauge group SU(N) and coupled to matter fields. For Chern-Simons level kk it is supposed to describe the worldvolume theory of NN coincident black M2-branes at an /k\mathbb{Z}/k-cyclic group orbifold singularity with near-horizon geometry AdS 4×S 7/(/k)AdS_4 \times S^7/(\mathbb{Z}/k) (see at M2-branes – As a black brane).

For k=2k = 2 the supersymmetry of the ABJM model increases to 𝒩=8\mathcal{N} = 8. For k=2k = 2 and N=2N = 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//k\mathbb{Z}/k (see also MFFGME 09).

Notice that the worldvolume SU(N)SU(N) gauge group enhancement at an k\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×S 7/ kAdS_4 \times S^7 / \mathbb{Z}_k.

Table of branes appearing in supergravity/string theory (for classification see at brane scan).

branein supergravitycharged under gauge fieldhas worldvolume theory
black branesupergravityhigher gauge fieldSCFT
D-branetype IIRR-fieldsuper Yang-Mills theory
(D=2n)(D = 2n)type IIA\,\,
D0-brane\,\,BFSS matrix model
D4-brane\,\,D=5 super Yang-Mills theory with Khovanov homology observables
D6-brane\,\,D=7 super Yang-Mills theory
(D=2n+1)(D = 2n+1)type IIB\,\,
D1-brane\,\,2d CFT with BH entropy
D3-brane\,\,N=4 D=4 super Yang-Mills theory
(D25-brane)(bosonic string theory)
NS-branetype I, II, heteroticcircle n-connection\,
string\,B2-field2d SCFT
NS5-brane\,B6-fieldlittle string theory
D-brane for topological string\,
M-brane11D SuGra/M-theorycircle n-connection\,
M2-brane\,C3-fieldABJM theory, BLG model
M5-brane\,C6-field6d (2,0)-superconformal QFT
M9-brane/O9-planeheterotic string theory
topological M2-branetopological M-theoryC3-field on G2-manifold
topological M5-brane\,C6-field on G2-manifold
solitons on M5-brane6d (2,0)-superconformal QFT
self-dual stringself-dual B-field
3-brane in 6d


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

Classification of the possible superpotentials? via representation theory is due to

and derived from this a classification of the possble orbifolding is in

See also

Computation of black hole entropy in 4d via AdS4-CFT3 duality from holographic entanglement entropy in the ABJM theory for the M2-brane is discussed in

  • Jun Nian, Xinyu Zhang, Entanglement Entropy of ABJM Theory and Entropy of Topological Black Hole (arXiv:1705.01896)

Revised on September 12, 2017 01:45:47 by Urs Schreiber (