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ABJM theory

Context

\infty-Chern-Simons theory

∞-Chern-Weil theory

∞-Chern-Simons theory

∞-Wess-Zumino-Witten theory

Ingredients

Definition

Examples

String theory

Contents

Idea

The ABJM model (ABJM 08) is 3-dimensional supersymmetric Chern-Simons theory with gauge group SU(N) and coupled to matter fields. It is supposed to describe the worldvolume theory of NN coincident M2-branes at an k\mathbb{Z}_k orbifold singularity. For N=2N = 2 it reduces to the BLG model. 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 matches 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).

Properties

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
D2-brane\,\,\,
D4-brane\,\,D=5 super Yang-Mills theory with Khovanov homology observables
D6-brane\,\,
D8-brane\,\,
(D=2n+1)(D = 2n+1)type IIB\,\,
D(-1)-brane\,\,\,
D1-brane\,\,2d CFT with BH entropy
D3-brane\,\,N=4 D=4 super Yang-Mills theory
D5-brane\,\,\,
D7-brane\,\,\,
D9-brane\,\,\,
(p,q)-string\,\,\,
(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\,
A-brane\,
B-brane\,
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
M-wave
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

References

The original article is

Discussion of the model as a higher gauge theory (due to its coupling to the supergravity C-field) is in

Discussion of the possible orbifolding is in

See also

  • Nadav Drukker, Marcos Marino, Pavel Putrov, From weak to strong coupling in ABJM theory (arXiv:1007.3837)

Revised on August 25, 2015 04:16:24 by Urs Schreiber (147.231.89.193)