We study the SO(8) superconformal theory proposed recently by Bagger and Lambert as a possible worldvolume theory for multiple M2-branes. For their explicit example with gauge group SO(4), we rewrite the theory (originally formulated in terms of a three-algebra) as an ordinary SU(2) \times SU(2) gauge theory with bifundamental matter. In this description, the parity invariance of the theory, required for a proper description of M2-branes, is clarified. We describe the subspace of scalar field configurations on which the potential vanishes, and note that this does not coincide with the moduli space for a stack of M2-branes. Finally, we point out a difficulty in constructing the required set of superconformal primary operators which should be present in the correct theory describing multiple M2-branes.
It is known that the M2-brane worldvolume superalgebra includes two p-form central charges that encode the M-theory intersections involving M2-branes. In this paper we show by explicit computation that the Bagger-Lambert Lagrangian realizes the M2-brane superalgebra, including also the central extensions. Solitons of the Bagger-Lambert theory, that are interpreted as worldvolume realizations of intersecting branes, are shown to saturate a BPS-bound given in terms of the corresponding central charge.
In this note, we discuss membrane scattering from the three dimensional N=8 superconformal theory with SO(8) global symmetry constructed by Bagger-Lambert and Gustavsson. We discuss whether the one loop effective potential consistently reproduces the Newton potential of membranes moving in an eleven dimensional orbifold space.
Among newly discovered M2, M5 objects in the Bagger-Lambert-Gustavsson theory, our interest is about half BPS vortices which are covariantly holomorphic curves in transverse coordinates. We restrict ourselves to the case where the global symmetry is broken to so(2) x so(2)x so(4) for the mass deformed Bagger-Lambert theory. A localized object with finite energy exists in this theory where the mass parameter supports regularity. It is time independent but carries angular momentum coming solely from the gauge potential by which the energy is bounded below.
We rewrite the Bagger-Lambert action for any Lie 3-algebra as a standard Chern- Simons action coupled to matter. We use this action to compute self-energies and vertex corrections at one-loop order. Non-renormalization of the coupling constant comes out as a direct consequence of the Lie 3-algebra structure underlying the Lie algebra.
In this paper we analyse the Bagger-Lambert-Gustavsson (BLG) theory in $\mathcal{N} =1$ superspace. Furthermore, we will construct the BRST transformations for this theory. These BRST transformations will be integrated out to obtain the finite field dependent version of BRST (FFBRST) transformations. We will also analyse the effect of the FFBRST transformations on the effective action. We will thus show that the FFBRST transformations can be used to relate generating functionals of the BLG theory in two different gauges.
We reformulate the Bagger-Lambert-Gustavsson model using an N=8 superspace, thus making the full supersymmetry manifest. The formulation is based on appropriate "pure spinor wave functions" for the Chern-Simons and matter multiplets. The Lagrangian has an extremely simple structure, essentially containing a Chern-Simons-like term for the gauge field wave function and a minimally coupled matter wave function. No higher order interactions than cubic are present. The consistency of the setup relies on an interplay between the algebraic structures of the 3-algebra and of the pure spinors.
We find a sixteen supersymmetric mass-deformed Bagger-Lambert theory with $SO(4)\times SO(4)$ global R-symmetry. The R-charge plays the `non-central' term in the superalgebra. This theory has one symmetric vacuum and two in-equivalent broken sectors of vacua. Each sector of the broken symmetry has the SO(4) geometry. We find the 1/2 BPS domain walls connecting the symmetric phase and any broken phase, and 1/4 BPS supertube-like objects, which may appear as anyonic q-balls in the symmetric phase or vortices in the broken phase. We also discuss mass deformations which reduces the number of super…
We continue our study of BPS equations and supersymmetric configurations in the Bagger-Lambert theory. The superalgebra allows three different types of central extensions which correspond to compounds of various M-theory objects: M2-branes, M5-branes, gravity waves and Kaluza-Klein monopoles which intersect or have overlaps with the M2-branes whose dynamics is given by the Bagger-Lambert action. As elementary objects they are all 1/2-BPS, and multiple intersections of $n$-branes generically break the supersymmetry into $1/2^n$, as it is well known. But a particular composite of M-branes can pr…
We study the structure of the gauge sector of the Bagger-Lambert-Gustavsson (BLG) theory in the form proposed by van Raamsdonk, adapted to 3D, N=1 superspace. By using the novel Higgs mechanism proposed by Mukhi and Papageorgakis, we derive the manifestly N=1 supersymmetric higher-order terms (beyond the supersymmetric Yang-Mills action) that follow from the BLG theory in its expansion with respect to the inverse gauge coupling constant squared. We find that all those terms have at least one anti-commutator of the super-YM field strength superfields as a factor, and thus are reducible to the S…
By compactifying the Bagger-Lambert-Gustavsson model on $\mathbb{R}^{1,1} \times S^1$, we obtain a new two dimensional massless field theory with dynamical fields valued in the Lie 3-algebra $\mathcal{A}$ coupled with an SO(1,1) scalar and vector field which are valued in the set $End(\mathcal{A})$ of the endomorphisms of the Lie 3-algebra. In the limit $g_{BLG} \to \infty$ the theory reduces to a supersymmetric Lie 3-valued generalization of the Green-Schwarz superstring in the light-cone gauge.
We classify, in a group theoretical manner, the BPS configurations in the multiple M2-brane theory recently proposed by Bagger and Lambert. We present three types of BPS equations preserving various fractions of supersymmetries: in the first type we have constant fields and the interactions are purely algebraic in nature; in the second type the equations are invariant under spatial rotation SO(2), and the fields can be time-dependent; in the third class the equations are invariant under boost SO(1,1) and provide the eleven-dimensional generalizations of the Nahm equations. The BPS equations fo…
We present two alternative field contents for Bagger-Lambert theory, based on the triality of SO(8). The first content is (φ_{A a}, χ_{\dot A a} ; A_\m{}^{a b}), where the bosonic field φis in the 8_S of SO(8) instead of the 8_V as in the original Bagger-Lambert formulation. The second field content is (φ_{\dot A a}, χ^I{}_a ; A_\m{}^{a b}), where the bosonic field φand the fermionic field χare respectively in the 8_C and 8_V of SO(8). In both of these field contents, the bosonic potentials are positive definite, as desired. Moreover, these bosonic potentials can be unified by the triality of …
We consider how to take an orbifold reduction for the multiple M2-brane theory recently proposed by Bagger and Lambert, and discuss its relation to Chern-Simons theories. Starting from the infinite dimensional 3-algebra realized as the Nambu bracket on a 3-torus, we first suggest an orbifolding prescription for various fields. Then we introduce a second truncation, which effectively reduces the internal space to a 2-torus. Eventually one obtains a large-N limit of Chern-Simons gauge theories coupled to matter fields. We consider an abelian orbifold C^4/Z_n, and illustrate how one can arrive at…
In this paper we will discuss the effect of a having a boundary on the supersymmetric invariance and gauge invariance of the Bagger-Lambert-Gustavsson (BLG) Theory. We will show that even though the supersymmetry and gauge invariance of the original BLG theory is broken due to the presence of a boundary, it restored by the addition of suitable boundary terms. In fact, to achieve the gauge invariance of this theory, we will have to introduce new boundary degrees of freedom. The boundary theory obeyed by these new boundary degrees of freedom will be shown to be a generalization of the gauged Wes…
In arXiv:0806.0363 the worldvolume superalgebra of the $\mathcal{N}=8$ Bagger-Lambert theory was calculated. In this paper we derive the general form for the worldvolume superalgebra of the $\mathcal{N}=6$ Bagger-Lambert theory. For a particular choice of three-algebra we derive the superalgebra of the ABJM theory. We interpret the associated central charges in terms of BPS brane configurations. In particular we find the central charge corresponding to the energy bound of the BPS fuzzy-funnel configuration of the ABJM theory. We also derive general expressions for the BPS equations of the $\ma…
We show that the N=8 superconformal Bagger-Lambert theory based on the Lorentzian 3-algebra can be derived by taking a certain scaling limit of the recently proposed N=6 superconformal U(N)xU(N) Chern-Simons-matter theories at level (k, -k). The scaling limit (and Inonu-Wigner contraction) is to scale the trace part of the bifundamental fields as X_0 -> λ^{-1} X_0 and an axial combination of the two gauge fields as B_μ -> λB_μ. Simultaneously we scale the level as k -> λ^{-1} k and then take λ-> 0 limit. Interestingly the same constraint equation \partial^2 X_0=0 is derived by imposing finiten…
We construct the totally antisymmetric structure constants f^{ABCD} of a 3-algebra with a Lorentzian bi-invariant metric starting from an arbitrary semi-simple Lie algebra. The structure constants f^{ABCD} can be used to write down a maximally superconformal 3d theory that incorporates the expected degrees of freedom of multiple M2 branes, including the "center-of-mass" mode described by free scalar and fermion fields. The gauge field sector reduces to a three dimensional BF term, which underlies the gauge symmetry of the theory. We comment on the issue of unitarity of the quantum theory, whic…
We classify Lie 3-algebras possessing an invariant lorentzian inner product. The indecomposable objects are in one-to-one correspondence with compact real forms of metric semisimple Lie algebras. We analyse the moduli space of classical vacua of the Bagger-Lambert theory corresponding to these Lie 3-algebras. We establish a one-to-one correspondence between one branch of the moduli space and compact riemannian symmetric spaces. We analyse the asymptotic behaviour of the moduli space and identify a large class of models with moduli branches exhibiting the desired N^{3/2} behaviour.
We prove a structure theorem for finite-dimensional indefinite-signature metric 3-Lie algebras admitting a maximally isotropic centre. This algebraic condition indicates that all the negative-norm states in the associated Bagger-Lambert theory can be consistently decoupled from the physical Hilbert space. As an immediate application of the theorem, new examples beyond index 2 are constructed. The lagrangian for the Bagger-Lambert theory based on a general physically admissible 3-Lie algebra of this kind is obtained. Following an expansion around a suitable vacuum, the precise relationship betw…
We recast physical properties of the Bagger-Lambert theory, such as shift-symmetry and decoupling of ghosts, the absence of scale and parity invariance, in Lie 3-algebraic terms, thus motivating the study of metric Lie 3-algebras and their Lie algebras of derivations. We prove a structure theorem for metric Lie 3-algebras in arbitrary signature showing that they can be constructed out of the simple and one-dimensional Lie 3-algebras iterating two constructions: orthogonal direct sum and a new construction called a double extension, by analogy with the similar construction for Lie algebras. We …
We review various generalizations of the notion of Lie algebras, in particular those appearing in the recently proposed Bagger-Lambert-Gustavsson model, and study their interrelations. We find that Filippov's n-Lie algebras are a special case of strong homotopy Lie algebras. Furthermore, we define a class of homotopy Maurer-Cartan equations, which contains both the Nahm and the Basu-Harvey equations as special cases. Finally, we show how the super Yang-Mills equations describing a Dp-brane and the Bagger-Lambert-Gustavsson equations supposedly describing M2-branes can be rewritten as homotopy …
This thesis consists of two parts. In the first part we investigate the worldvolume supersymmetry algebra of multiple membrane theories. We begin with a description of M-theory branes and their intersections from the perspective of spacetime and worldvolume supersymmetry algebras. We then provide an overview of the recent work on multiple M2-branes focusing on the Bagger-Lambert theory and its relation to the Nambu-Poisson M5-brane and the ABJM theory. The worldvolume supersymmetry algebras of these theories are explicitly calculated and the charges interpreted in terms of spacetime intersecti…
We show that the Bagger-Lambert theory of multiple M2-branes fits into the general construction of maximally supersymmetric gauge theories using the embedding tensor technique. We apply the embedding tensor technique in order to systematically obtain the consistent gaugings of N=8 superconformal theories in 2+1 dimensions. This leads to the Bagger-Lambert theory, with the embedding tensor playing the role of the four-index antisymmetric tensor defining a ``3-algebra''. We present an alternative formulation of the theory in which the embedding tensor is replaced by a set of unrestricted scalar …
We elaborate on the suggestion made in arXiv:0806.3498 that the 3d \N=8 superconformal SU(N) Chern-Simons-matter theory of Lorentzian Bagger-Lambert-Gustavson type (L-BLG) can be obtained by a scaling limit (involving sending the level k to infinity and redefining the fields) from the \N=6 superconformal U(N)xU(N) Chern-Simons-matter theory of Aharony, Bergman, Jafferis and Maldacena (ABJM). We show that to implement such a limit in a consistent way one is to extend the ABJM theory by an abelian "ghost" multiplet. The corresponding limit at the 3-algebra level also requires extending the non-a…
Bagger-Lambert-Gustavsson theory with infinite dimensional gauge group has been suggested to describe M5-brane as a condensation of multiple M2-branes. Here we perform a topological twisting of the Bagger-Lambert-Gustavsson theory. The original SO(8) R-symmetry is broken to SO(3)XSO(5), where the former may be interpreted as a diagonal subgroup of the Euclidean M5-brane world-volume symmetry SO(6), while the latter is the isometry of the transverse five directions. Accordingly the resulting action contains an one-form and five scalars as for the bosonic dynamical fields. We further lift the ac…
The recently formulated Bagger-Lambert-Gustavsson (BLG) theory in three dimensions is described in terms of a constrained chiral superfield in light-cone superspace. We discuss the use of Superconformal symmetry to determine the form of its interactions, in complete analogy with N=4 SuperYang-Mills in four dimensions.
We present an octonionic N=1 superfield action that reproduces in components the action of Bagger and Lambert for M2 branes. By giving an expectation value to one of the scalars we obtain the maximally supersymmetric superfield action for D2 branes.
This paper examines various aspects of the recently proposed theory of coincident membranes by Bagger and Lambert. These include the properties of open membranes and the resulting boundary theory with an interpretation in terms of the fivebrane and marginal supersymmetric deformations of the interactions with the relation to the holographic dual.
The light-cone superspace version of the d=3, N=8 superconformal theory of Bagger, Lambert and Gustavsson (BLG) is obtained as a solution to constraints imposed by OSp(2,2|8) superalgebra. The Hamiltonian of the theory is shown to be a quadratic form of the dynamical supersymmetry transformation.
We construct an alternative form of the M5-brane action in which the six-dimensional worldvolume is subject to a covariant split into 3+3 directions by a triplet of auxiliary fields. We consider the relation of this action to the original form of the M5-brane action and to a Nambu-Poisson 5-brane action based on the Bagger-Lambert-Gustavsson model with the gauge symmetry of volume preserving diffeomorphisms
Since the pioneering work of Bagger-Lambert and Gustavsson, there has been a proliferation of three-dimensional superconformal Chern-Simons theories whose main ingredient is a metric 3-algebra. On the other hand, many of these theories have been shown to allow for a reformulation in terms of standard gauge theory coupled to matter, where the 3-algebra does not appear explicitly. In this paper we reconcile these two sets of results by pointing out the Lie-algebraic origin of some metric 3-algebras, including those which have already appeared in three-dimensional superconformal Chern-Simons theo…
We give a concise review of recent developments of the M5-brane theory derived from the Bagger-Lambert model. It is a 6 dimensional supersymmetric self-dual gauge theory describing an M5-brane in a large constant $C$-field background. The non-Abelian gauge symmetry corresponds to diffeomorphisms preserving an exact 3-form on the worldvolume, which defines a Nambu-Poisson bracket. Various interesting geometric and algebraic properties of the theory are discussed.
We classify canonical metric 3-algebra structures on matrix algebras and find novel three-dimensional conformally invariant actions in N=4 projective superspace based on them. These can be viewed as Chern-Simons theories with special matter content and couplings. We explore the relations of these actions with the N=2 actions based on generalized 3-Lie algebras found earlier and relate them to the original Bagger-Lambert-Gustavsson action.
We investigate space-time supersymmetry of the model of multiple M2-branes proposed by Bagger-Lambert and Gustavsson. When there is a central element in Lie 3-algebra, the model possesses an extra symmetry shifting the fermions in the central element. Together with the original worldvolume supersymmetry transformation, we construct major part of the eleven dimensional space-time super-Poincaré algebra with central extensions. Implications to transverse five-branes in the matrix model for M-theory are also discussed.
We investigate supersymmetric boundary conditions in both the Bagger-Lambert and the ABJM theories of interacting membranes. We find boundary conditions associated to the fivebrane, the ninebrane and the M-theory wave. For the ABJM theory we are able to understand the enhancement of supersymmetry to produce the (4,4) supersymmetry of the self-dual string. We also include supersymmetric boundary conditions on the gauge fields that cancel the classical gauge anomaly of the Chern-Simons terms.
Recently it was proposed that the Bagger-Lambert-Gustavsson theory with Nambu-Poisson structure describes an M5-brane in a three-form flux background. In this paper we investigate the superalgebra associated with this theory. We derive the central charges corresponding to M5-brane solitons in 3-form backgrounds. We also show that double dimensional reduction of the superalgebra gives rise to the Poisson bracket terms of a non-commutative D4-brane superalgebra. We provide interpretations of the D4-brane charges in terms of spacetime intersections.
As we re-examine the known holographic N=1 supersymmetric renormalization group flow in four dimensions, we describe the mass-deformed Bagger-Lambert theory or equivalently the mass-deformed U(2) x U(2) Chern-Simons gauge theory with level k=1 or 2, that has G_2 symmetry, by adding a mass term for one of the eight adjoint superfields. We obtain a detailed correspondence between the fields of AdS_4 supergravity and composite operators of the infrared field theory in three dimensions. The geometric superpotential from an eleven dimensional viewpoint is obtained for M2-brane probe analysis.
We propose a generalization of the Bagger-Lambert-Gustavsson action as a candidate for the description of an arbitrary number of M2-branes. The action is formulated in terms of N=2 superfields in three dimensions and corresponds to an extension of the usual superfield formulation of Chern-Simons matter theories. Demanding gauge invariance of the resulting theory does not imply the total antisymmetry of the underlying 3-Lie algebra structure constants. We relax this condition and propose a class of examples for these generalized 3-Lie algebras. We also discuss how to associate various ordinary …
Motivated by the recent proposal of an N=8 supersymmetric action for multiple M2-branes, we study the Lie 3-algebra in detail. In particular, we focus on the fundamental identity and the relation with Nambu-Poisson bracket. Some new algebras not known in the literature are found. Next we consider cubic matrix representations of Lie 3-algebras. We show how to obtain higher dimensional representations by tensor products for a generic 3-algebra. A criterion of reducibility is presented. We also discuss the application of Lie 3-algebra to the membrane physics, including the Basu-Harvey equation an…
Maximally supersymmetric mass deformation of the Bagger-Lambert-Gustavsson (BLG) theory corresponds to a {non-central} extension of the d=3 N=8 Poincare superalgebra (allowed in three dimensions). We obtain its light-cone superspace formulation which has a novel feature of the dynamical supersymmetry generators being {cubic} in the kinematical ones. The mass deformation picks a quaternionic direction, which breaks the SO(8) R-symmetry down to SO(4)xSO(4). The Hamiltonian of the theory is shown to be a quadratic form of the dynamical supersymmetry transformations, to all orders in the mass para…
Studying the supersymmetry enhancement mechanism of Aharony, Bergman, Jafferis and Maldacena, we find a simple condition on the gauge group generators for the matter fields. We analyze all possible compact Lie groups and their representations. The only allowed gauge groups leading to the manifest N=6 supersymmetry are, up to discrete quotients, SU(n) x U(1), Sp(n) x U(1), SU(n) x SU(n), and SU(n) x SU(m) x U(1) with possibly additional U(1)'s. Matter representations are restricted to be the (bi)fundamentals. As a byproduct we obtain another proof of the complete classification of the three alg…
We extend the N=4 superconformal Chern-Simons theories of Gaiotto and Witten to those with additional twisted hyper-multiplets. The new theories are generically linear quiver gauge theories with the two types of hyper-multiplets alternating between gauge groups. Our construction includes the Bagger-Lambert model of SO(4) gauge group. A family of abelian theories are identified with those proposed earlier in the context of the M-crystal model for M2-branes probing (C^2/Z_n)^2 orbifolds. Possible extension with non-abelian BF couplings and string/M-theory realization are briefly discussed.
By coupling {\cal N}=8 superconformal matter to {\cal N}=8 superconformal Chern-Simons gravity in three dimensions we obtain theories with novel terms in the scalar potential leading to AdS_3 solutions and superconformal symmetry breaking. If we start from the theory derived by Bagger, Lambert and Gustavsson, our coupled theory either inherits the SO(4) gauge group or reduces it to SO(3). If the construction is instead based on a free matter theory we find that the gravitational topological gauging also requires the introduction of a Chern-Simons gauge sector resulting in a consistent theory f…
The Bagger--Lambert construction of N = 8 superconformal field theories (SCFT) in three dimensions is based on 3-algebras. Three groups of researchers recently realized that an arbitrary semisimple Lie algebra can be incorporated by using a suitable Lorentzian signature 3-algebra. The SU(N) case is a candidate for the SCFT describing coincident M2-branes. However, these theories contain ghost degrees of freedom, which is unsatisfactory. We modify them by gauging certain global symmetries. This eliminates the ghosts from these theories while preserving all of their desirable properties. The res…
In this short note, we reduce the N=6, U(N)xU(N) Chern-Simons gauge theories to N=8, U(N) Yang-Mills gauge theories. This process corresponds to recovering the world-volume theory of N D2-branes from that of N M2-branes in an intermediate energy range. The supersymmetries are enhanced because in this limit the branes localize far away from the orbifold singularity. Our main scheme is exactly in accordance with Mukhi and Papageorgakis's earlier work, although the Higgs mechanism becomes trickier in the present case. We also speculate on applying the scheme to a large class of new Bagger-Lambert…
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 theor…
We argue that the moduli space for the Bagger-Lambert A_4 theory at level k is (R^8 \times R^8)/D_{2k}, where D_{2k} is the dihedral group of order 4k. We conjecture that the theory describes two M2-branes on a Z_{2k} ``M-fold'', in which a geometrical action of Z_{2k} is combined with an action on the branes. For k=1, this arises as the strong coupling limit of two D2-branes on an O2^- orientifold, whose worldvolume theory is the maximally supersymmetric SO(4) gauge theory. Finally, in an appropriate large-k limit we show that one recovers compactified M-theory and the M2-branes reduce to D2-…
We investigate the Bagger-Lambert-Gustavsson model associated with the Nambu-Poisson algebra as a theory describing a single M5-brane. We argue that the model is a gauge theory associated with the volume-preserving diffeomorphism in the three-dimenisonal internal space. We derive gauge transformations, actions, supersymmetry transformations, and equations of motions in terms of six-dimensional fields. The equations of motions are written in gauge-covariant form, and the equations for tensor fields have manifest self-dual structure. We demonstrate that the double dimensional reduction of the mo…
This paper is concerned with the problem of coupling the N=8 superconformal Bagger-Lambert-Gustavsson (BLG) theory to N=8 conformal supergravity in three dimensions. We start by constructing the on-shell N=8 conformal supergravity in three dimensions consisting of a Chern-Simons type term for each of the gauge fields: the spin connection, the SO(8) R-symmetry gauge field and the spin 3/2 Rarita-Schwinger (gravitino) field. We then proceed to couple this theory to the BLG theory. The final theory should have the same physical content, i.e., degrees of freedom, as the ordinary BLG theory. We dis…
We present a manifestly SO(8) invariant non-linear Lagrangian for describing the non-abelian dynamics of the bosonic degrees of freedom of N coinciding M2 branes in flat spacetime. The theory exhibits a gauge symmetry structure of the BF type (semidirect product of SU(N) and translations) and at low energies it reduces exactly to the bosonic part of the Lorentzian Bagger-Lambert Lagrangian for group SU(N). There are eight scalar fields satisfying a free-scalar equation. When one of them takes a large expectation value, the non-linear Lagrangian gets simplified and the theory can be connected t…
We reveal non-manifest gauge and SO(1,5) Lorentz symmetries in the Lagrangian description of a six-dimensional free chiral field derived from the Bagger-Lambert-Gustavsson model in arXiv:0804.3629 and make this formulation covariant with the use of a triplet of auxiliary scalar fields. We consider the coupling of this self-dual construction to gravity and its supersymmetrization. In the case of the non-linear model of arXiv:0805.2898 we solve the equations of motion of the gauge field, prove that its non-linear field strength is self-dual and find a gauge-covariant form of the non-linear actio…
We investigate conformal symmetries of the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory for multiple M2 branes and the Lorentzian Bagger-Lambert-Gustavsson (L-BLG) theory which can be obtained by taking a scaling limit k (>>N) -> \infty of the ABJM theory. The conformal symmetry is maintained in the L-BLG by considering general space-time varying solutions to the constraint equations. The dual geometry is reduced to d=10 AdS4 x CP3 in the scaling limit and has the same conformal symmetry. The curvature radius R satisfies l_{11p} << l_{10p} << R << l_s (l_{dp} and l_s are the d-dimensional …
We present two derivations of the multiple D2 action from the multiple M2-brane model proposed by Bagger-Lambert and Gustavsson. The first one is to start from Lie 3-algebra associated with given (arbitrary) Lie algebra. The Lie 3-algebra metric is not positive definite but the zero-norm generators merely correspond to Lagrange multipliers. Following the work of Mukhi and Papageorgakis, we derive D2-brane action from the model by giving a variable a vacuum expectation value. The second derivation is based on the correspondence between M2 and M5. We compactify one dimension and wind M5 brane al…
Based on the recent proposal of N=8 superconformal gauge theories of the multiple M2 branes, we derive (2+1)-dimensional supersymmetric Janus field theories with a space-time dependent coupling constant. From the original Bagger-Lambert model, we get a supersymmetric field theory with a similar action to the N D2 branes, but the coupling varies with the space-time as a function of the light-cone coordinate, g(t+x). Half of the supersymmetries can be preserved. We further investigate the M2 brane action deformed by mass and Myers-like terms. In this case, the final YM action is deformed by mass…
We discuss the N=2 superspace formulation of the N=8 superconformal Bagger-Lambert-Gustavsson theory, and of the N=6 superconformal Aharony-Bergman-Jafferis-Maldacena U(N)xU(N) Chern-Simons theory. In particular, we prove the full SU(4) R-symmetry of the ABJM theory. We then consider orbifold projections of this theory that give non-chiral and chiral (U(N)xU(N))^n superconformal quiver gauge theories. We argue that these theories are dual to certain AdS_4 x S^7/(Z_n x Z_k) backgrounds of M-theory. We also study a SU(3) invariant mass term in the superpotential that makes the N=8 theory flow to…
We construct three dimensional Chern-Simons-matter theories with gauge groups U(N)xU(N) and SU(N)xSU(N) which have explicit N=6 superconformal symmetry. Using brane constructions we argue that the U(N)xU(N) theory at level k describes the low energy limit of N M2-branes probing a C^4/Z_k singularity. At large N the theory is then dual to M theory on AdS_4xS^7/Z_k. 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 AdS_4xCP^3. For k=1 the theory is conjectured to describe N M2-branes in flat space, although our construction realiz…
We study the detail derivation of the multiple D2-brane effective action from multiple M2-branes in the Bagger-Lambert-Gustavsson (BLG) theory and the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory by employing the novel Higgs mechanism. We show explicitly that the high-order F^3 and F^4 terms are commutator terms, and conjecture that all the high-order terms are commutator terms. Because the commutator terms can be treated as the covariant derivative terms, these high-order terms do not contribute to the multiple D2-brane effective action. Inspired by the derivation of a single D2-brane fro…
We give a brief review of Bagger-Lambert-Gustavsson (BLG) model, with emphasis on its version invariant under the volume preserving diffeomorphisms (SDiff3) symmetry. We describe the on-shell superfield formulation of this SDiff3 BLG model in standard N=8, d=3 superspace, as well as its superfield action in the pure spinor N=8 superspace. We also briefly address the Aharony-Bergman-Jafferis-Maldacena (ABJM/ABJ) model invariant under $SU(M)_{k}\times SU(N')_{-k}$ gauge symmetry, and discuss the possible form of their N=6 and, for the case of Chern-Simons level k=1,2, N=8 superfield equations.
Based on the realization of three-algebras in terms of algebra of matrices and four-brackets [arXiv:0807.1570] we present the notion of u(N)-based extended three-algebras, which for N=2 reproduces the Bagger-Lambert three-algebra. Using these extended three-algebras we construct an su(N)\times su(N) Chern-Simons action with explicit SO(8) invariance. The dynamical fields of this theory are eight complex valued bosonic and fermionic fields in the bi-fundamental representation of the su(N)\times su(N). For generic N the fermionic transformations, however, close only on a subclass of the states o…
