M2-branes, Einstein Manifolds and Triple Systems

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.

Nuclear Physics B, 2001

The purpose of this Letter is to continue the study of the class of models proposed in the previous paper [1] hep-th/0002077. The model corresponds to a system of branes of diverse dimensionalities with Chern-Simons actions for a supergroup, embedded in a background described also by a Chern-Simons action. The model treats the background and the branes on an equal footing, providing a 'brane-target space democracy'. Here we suggest some possible extensions of the original model, and disscuss its equations of motion, as well as the issue of currents and charges carried by the branes. We also disscuss the relationship with M-theory and Superstring theory.

Nuclear Physics B, 2002

We obtain a generalisation of the original complete Ricci-flat metric of G 2 holonomy on R 4 × S 3 to a family with a non-trivial parameter λ. For generic λ the solution is singular, but it is regular when λ = {−1, 0, +1}. The case λ = 0 corresponds to the original G 2 metric, and λ = {−1, 1} are related to this by an S 3 automorphism of the SU (2) 3 isometry group that acts on the S 3 × S 3 principal orbits. We then construct explicit supersymmetric M3-brane solutions in D = 11 supergravity, where the transverse space is a deformation of this class of G 2 metrics. These are solutions of a system of first-order differential equations coming from a superpotential. We also find M3-branes in the deformed backgrounds of new G 2-holonomy metrics that include one found by A. Brandhuber, J. Gomis, S. Gubser and S. Gukov, and show that they also are supersymmetric.

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.

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.

Physics Letters B, 2000

We present warped metrics which solve Einstein equations with arbitrary cosmological constants in both in upper and lower dimensions. When the lower-dimensional metric is the maximally symmetric one compatible with the chosen value of the cosmological constant, the upper-dimensional metric is also the maximally symmetric one and there is maximal unbroken supersymmetry as well.

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.

Journal of High Energy Physics, 2008

Due to the difficulties of finding superconformal Lagrangian theories for multiple M2-branes, we will in this paper instead focus on the field equations. By relaxing the requirement of a Lagrangian formulation we can explore the possibility of having structure constants $f^{ABC}{}_D$ satisfying the fundamental identity but which are not totally antisymmetric. We exemplify this discussion by making use of an explicit choice of a non-antisymmetric $f^{ABC}{}_D$ constructed from the Lie algebra structure constants $f^{ab}{}_c$ of an arbitrary gauge group. Although this choice of $f^{ABC}{}_D$ does not admit an obvious Lagrangian description, it does reproduce the correct SYM theory for a stack of $N$ D2-branes to leading order in $g_{YM}^{-1}$ upon reduction and, moreover, it sheds new light on the centre of mass coordinates for multiple M2-branes.

Physical Review D, 2009

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.

Journal of High Energy Physics, 2009

We study non-relativistic limits of the N = 6 Chern-Simons-Matter theory that arises as a low-energy limit of the M2-brane gauge theory with background flux. The model admits several different non-relativistic limits and we find that the maximal supersymmetry we construct has 14 components of supercharges, which is a novel example of non-relativistic superconformal algebra in (1 + 2) dimension. We also investigate the other limits that realize less supersymmetries.