Gauge symmetry and supersymmetry of multiple M2-branes
TL;DR: In this article, a supersymmetric field theory model for multiple M2-branes based on an algebra with a totally antisymmetric triple product is proposed. But the field is not dynamical.
Abstract: In previous work we proposed a field theory model for multiple M2-branes based on an algebra with a totally antisymmetric triple product. In this paper we gauge a symmetry that arises from the algebra's triple product. We then construct a supersymmetric theory with no free parameters that is consistent with all the continuous symmetries expected of a multiple M2-brane theory: 16 supersymmetries, conformal invariance, and an SO(8) R-symmetry that acts on the eight transverse scalars. The gauge field is not dynamical. The result is a new type of maximally supersymmetric gauge theory in three dimensions.
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TL;DR: In this paper, the authors constructed three dimensional Chern-Simons-matter theories with gauge groups U(N) × U(n) and SU(N), SU(2) × SU (2) which have explicit = 6 superconformal symmetry.
Abstract: We construct three dimensional Chern-Simons-matter theories with gauge groups U(N) × U(N) and SU(N) × SU(N) which have explicit = 6 superconformal symmetry. Using brane constructions we argue that the U(N) × U(N) theory at level k describes the low energy limit of N M2-branes probing a C4/Zk singularity. At large N the theory is then dual to M-theory on AdS4 × S7/Zk. The theory also has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type IIA string theory on AdS4 × CP3. For k = 1 the theory is conjectured to describe N M2-branes in flat space, although our construction realizes explicitly only six of the eight supersymmetries. We give some evidence for this conjecture, which is similar to the evidence for mirror symmetry in d = 3 gauge theories. When the gauge group is SU(2) × SU(2) our theory has extra symmetries and becomes identical to the Bagger-Lambert theory.
3,091 citations
TL;DR: In this paper, the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter were computed using localization techniques, and the path-integral reduces to a non-Gaussian matrix model.
Abstract: We use localization techniques to compute the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter. We find the path-integral reduces to a non-Gaussian matrix model. The Wilson loops we consider preserve a single complex supersymmetry, and exist in any N = 2 theory, though the localization requires superconformal symmetry. We present explicit results for the cases of pure Chern-Simons theory with gauge group U(N), showing agreement with the known results, and ABJM, showing agreement with perturbative calculations. Our method applies to other theories, such as Gaiotto-Witten theories, BLG, and their variants.
1,154 citations
Cites background from "Gauge symmetry and supersymmetry of..."
...This is the case for N = 4 theories of Gaiotto and Witten, the N = 6 ABJM theory, and the N = 8 BLG theory....
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...Closely related are the the theories of ABJM [2], with N = 6 SUSY, and BLG [3], with N = 8....
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...Our method applies to other theories, such as Gaiotto-Witten theories, BLG, and their variants....
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TL;DR: In this article, two generalizations of the = 6 superconformal Chern-Simons-matter theories with gauge group U(n) × U(N) have been considered, and they are conjectured to describe M−N| fractional M2-branes localized at the orbifold singularity.
Abstract: We consider two generalizations of the = 6 superconformal Chern-Simons-matter theories with gauge group U(N) × U(N). The first generalization is to = 6 superconformal U(M) × U(N) theories, and the second to = 5 superconformal O(2M) × USp(2N) and O(2M+1) × USp(2N) theories. These theories are conjectured to describe M2-branes probing C4/Zk in the unitary case, and C4/k in the orthogonal/symplectic case, together with a discrete flux, which can be interpreted as |M−N| fractional M2-branes localized at the orbifold singularity. The classical theories with these gauge groups have been constructed before; in this paper we focus on some quantum aspects of these theories, and on a detailed description of their M theory and type IIA string theory duals.
764 citations
TL;DR: In this paper, a series of lectures given at the KITP workshop Quantum Criticality and the AdS/CFT Correspondence in July 2009 were described, with the goal of the lectures being to introduce condensed matter physicists to the CFT correspondence.
Abstract: These are notes based on a series of lectures given at the KITP workshop Quantum Criticality and the AdS/CFT Correspondence in July, 2009. The goal of the lectures was to introduce condensed matter physicists to the AdS/CFT correspondence. Discussion of string theory and of supersymmetry is avoided to the extent possible.
635 citations
TL;DR: In this paper, the authors show that the planar free energy of ABJM theory matches the classical IIA supergravity action on a zero-dimensional super-matrix model and gives the correct N 3/2 scaling for the number of degrees of freedom of M2 brane theory.
Abstract: The partition function of $${\mathcal{N}=6}$$
supersymmetric Chern–Simons-matter theory (known as ABJM theory) on $${\mathbb{S}^3}$$
, as well as certain Wilson loop observables, are captured by a zero dimensional super-matrix model. This super–matrix model is closely related to a matrix model describing topological Chern–Simons theory on a lens space. We explore further these recent observations and extract more exact results in ABJM theory from the matrix model. In particular we calculate the planar free energy, which matches at strong coupling the classical IIA supergravity action on $${{\rm AdS}_4\times\mathbb{C}\mathbb{P}^3}$$
and gives the correct N
3/2 scaling for the number of degrees of freedom of the M2 brane theory. Furthermore we find contributions coming from world-sheet instanton corrections in $${\mathbb{C}\mathbb{P}^3}$$
. We also calculate non-planar corrections, both to the free energy and to the Wilson loop expectation values. This matrix model appears also in the study of topological strings on a toric Calabi–Yau manifold, and an intriguing connection arises between the space of couplings of the planar ABJM theory and the moduli space of this Calabi–Yau. In particular it suggests that, in addition to the usual perturbative and strong coupling (AdS) expansions, a third natural expansion locus is the line where one of the two ’t Hooft couplings vanishes and the other is finite. This is the conifold locus of the Calabi–Yau, and leads to an expansion around topological Chern–Simons theory. We present some explicit results for the partition function and Wilson loop observables around this locus.
608 citations
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01 Jan 2005
5,803 citations
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...1bagger@jhu.edu 2neil.lambert@kcl.ac.uk...
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TL;DR: In this article, the authors assume a certain algebraic structure for the low energy theory living on parallel M2 branes, and assume a topological degree-of-freedom field with topological degrees of freedom.
1,449 citations
TL;DR: In this article, the authors investigate the world volume theory that describes $N$ coincident M2-branes ending on an M5-brane and show how a Basu-Harvey fuzzy funnel arises as the Bogomol'nyi-Prasad-Sommerfield solution.
Abstract: We investigate the worldvolume theory that describes $N$ coincident M2-branes ending on an M5-brane. We argue that the fields that describe the transverse spacetime coordinates take values in a nonassociative algebra. We postulate a set of supersymmetry transformations and find that they close into a novel gauge symmetry. We propose a three-dimensional $N=2$ supersymmetric action to describe the truncation of the full theory to the scalar and spinor fields, and show how a Basu-Harvey fuzzy funnel arises as the Bogomol'nyi-Prasad-Sommerfield solution to this theory.
1,111 citations
TL;DR: In this paper, a Lagrangian description of a maximally supersymmetric conformal field theory in three dimensions was constructed recently by Bagger and Lambert (BL), which has SO(4) gauge symmetry and contains scalar and spinor fields that transform as 4-vectors.
Abstract: A Lagrangian description of a maximally supersymmetric conformal field theory in three dimensions was constructed recently by Bagger and Lambert (BL). The BL theory has SO(4) gauge symmetry and contains scalar and spinor fields that transform as 4-vectors. We verify that this theory has OSp(8|4) superconformal symmetry and that it is parity conserving despite the fact that it contains a Chern-Simons term. We describe several unsuccessful attempts to construct theories of this type for other gauge groups and representations. This experience leads us to conjecture the uniqueness of the BL theory. Given its large symmetry, we expect this theory to play a significant role in the future development of string theory and M-theory.
569 citations
TL;DR: In this paper, the possibilities for constructing Lagrangian descriptions of three-dimensional superconformal classical gauge theories that contain a Chern-Simons term, but no kinetic term, for the gauge fields are explored.
Abstract: We explore the possibilities for constructing Lagrangian descriptions of three-dimensional superconformal classical gauge theories that contain a Chern-Simons term, but no kinetic term, for the gauge fields. Classes of such theories with N = 1 and N = 2 supersymmetry are found. However, interacting theories of this type with N = 8 supersymmetry do not exist.
394 citations