On relating multiple M2 and D2-branes (original) (raw)

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𝒩 = 8 superconformal gauge theories and M 2 branes

Journal of High Energy Physics, 2009

Based on recent developments, in this letter we find 2 + 1 dimensional gauge theories with scale invariance and N = 8 supersymmetry. The gauge theories are defined by a lagrangian and are based on an infinite set of 3-algebras, constructed as an extension of ordinary Lie algebras. Recent no-go theorems on the existence of 3-algebras are circumvented by relaxing the assumption that the invariant metric is positive definite. The gauge group is non compact, and its maximally compact subgroup can be chosen to be any ordinary Lie group, under which the matter fields are adjoints or singlets. The theories are parity invariant and do not admit any tunable coupling constant. In the case of SU(N) the moduli space of vacua contains a branch of the form (R 8) N /S N. These properties are expected for the field theory living on a stack of M2 branes.

Script N = 8 superconformal gauge theories and M2 branes

Journal of High Energy Physics, 2009

Based on recent developments, in this letter we find 2+1 dimensional gauge theories with scale invariance and N=8 supersymmetry. The gauge theories are defined by a Lagrangian and are based on an infinite set of 3-algebras, constructed as an extension of ordinary Lie algebras. Recent no-go theorems on the existence of 3-algebras are circumvented by relaxing the assumption that the invariant metric is positive definite. The gauge group is non compact, and its maximally compact subgroup can be chosen to be any ordinary Lie group, under which the matter fields are adjoints or singlets. The theories are parity invariant and do not admit any tunable coupling constant. In the case of SU(N) the moduli space of vacua contains a branch of the form (R^8)^N/S_N. These properties are expected for the field theory living on a stack of M2 branes.

Multiple M2-branes and generalized 3-Lie algebras

Physical Review D, 2008

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 various associated ordinary Lie algebras.

Interaction between M2-branes and bulk form fields

Journal of High Energy Physics, 2010

We construct the interaction terms between the world-volume fields of multiple M2branes and the 3-and 6-form fields in the context of ABJM theory with U(N)×U(N) gauge symmetry. A consistency check is made in the simplest case of a single M2-brane i.e., our construction matches the known effective action of M2-brane coupled to antisymmetric 3-form field. We show that when dimensionally reduced, our couplings coincide with the effective action of D2-branes coupled to R-R 3-and 5-form fields in type IIA string theory. We also comment on the relation between a coupling with a specific 6-form field configuration and the supersymmetry preserving mass deformation in ABJM theory. Recently, the Lagrangian descriptions of multiple M2-branes were found in the low energy limit, which are the Bagger-Lambert-Gustavsson(BLG) theory [1, 2] and the Aharony-Bergman-Jafferis-Maldacena(ABJM) theory [3]. The BLG theory, which is equivalent to the ABJM theory with SU(2)×SU(2) gauge group [4], has N = 8 supersymmetry and it is an effective theory of two M2-branes. The ABJM theory with U(N)×U(N) gauge group has N = 6 supersymmetry and it describes the dynamics of N parallel M2-branes sitting at the singularity of a space with Z k orbifold, where k appears as the Chern-Simons level in the theory. Low energy dynamics of D-branes is also depicted by supersymmetric gauge theories, i.e., it is the Dirac-Born-Infeld(DBI) action or the super Yang-Mills theory to the leading order in α ′expansion. In addition, D-branes can couple to the bulk supergravity fields. The bosonic bulk fields include R-R form fields, which couple to the D-branes through Wess-Zumino(WZ)-type action [5, 6, 7]. In the case of single Dp-brane, the WZ-type coupling is only to the R-R form fields of rank p + 1 or less. For multiple Dp-branes the action can include the couplings to all kinds of R-R form fields [7].

Ghost-free superconformal action for multiple M 2-branes

Journal of High Energy Physics, 2008

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.

Algebraic structures on parallel M2 branes

Nuclear Physics B, 2009

In the course of closing supersymmetry on parallel M2 branes up to a gauge transformation, following the suggestion in hep-th/0611108 of incorporating a gauge field which only has topological degrees of freedom, we are led to assume a certain algebraic structure for the low energy theory supposedly living on parallel M2 branes.

On non-linear action of multiple M2-branes

Nuclear Physics B, 2009

A nonlinear SO(8) invariant BF type Lagrangian for describing the dynamics of N M2branes in flat spacetime has been proposed recently in the literature which is an extension of the non-abelian DBI action of N D2-branes. This action includes only terms with even number of the totally antisymmetric tensor M IJK . We argue that the action should contain terms with odd number of M IJL as well. We modify the action to include them.

𝒩 = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals

Journal of High Energy Physics, 2008

We construct three dimensional Chern-Simons-matter theories with gauge groups U (N ) ×U (N ) and SU (N ) ×SU (N ) which have explicit N = 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 C 4 /Z k singularity. At large N the theory is then dual to M-theory on AdS 4 × S 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 4 × CP 3 . 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.

Coupling between M2-branes and form fields

Journal of High Energy Physics, 2009

In the context of low-energy effective theory of multiple M2-branes, we construct the interaction terms between the world-volume fields of M2-branes and the antisymmetric tensor fields of three-and six-forms. By utilizing the compactification procedure, we show coincidence between the dimensionally reduced coupling and the R-R coupling to D-branes in type II string theory. We also discuss that a cubic term proportional to six-form field reproduces the quartic mass-deformation term in the world-volume theory of multiple M2-branes.

An SL(2,?)-covariant, first order, ?-supersymmetric action for theD5-brane

Fortschritte der Physik, 2005

The new first order, rheonomic, κ-supersymmetric formalism recently introduced by us for the world-volume action of the D3 brane is extended to the case of D5 branes. This extension requires the dual formulation of the Free Differential Algebra of type IIB supergravity in terms of 6-form gauge potentials which was so far missing and is given here. Furthermore relying on our new approach we are able to write the D5 world volume action in a manifestly SL(2, R) covariant form. This is important in order to solve the outstanding problem of finding the appropriate boundary actions of D3-branes on smooth ALE manifolds with twisted fields. The application of our results to this problem is however postponed to a subsequent publication.