Unifying N=5 and N=6

We write the Lagrangian of the general N=5 three-dimensional superconformal Chern-Simons theory, based on a basic Lie superalgebra, in terms of our recently introduced N=5 three-algebras. These include N=6 and N=8 three-algebras as special cases. When we impose an antisymmetry condition on the triple product, the supersymmetry automatically enhances, and the N=5 Lagrangian reduces to that of the well known N=6 theory, including the ABJM and ABJ models.Comment: 19 pages. v2: Published version. Minor typos corrected, references adde

N=2 Super-Born-Infeld from Partially Broken N=3 Supersymmetry in d=4

We employ the non-linear realization techniques to relate the N=1 chiral, and the N=2 vector multiplets to the Goldstone spin 1/2 superfield arising from partial supersymmetry breaking of N=2 and N=3 respectively. In both cases, we obtain a family of non-linear transformation laws realizing an extra supersymmetry. In the N=2 case, we find an invariant action which is the low energy limit of the supersymmetric Born-Infeld theory expected to describe a D3-brane in six dimensions.Comment: 15 pages, no figures, RevTeX4, new comments and references added, some equations corrected, discussion at end of sec. 3 change

Oblique DLCQ M-theory and Multiple M2-branes

We propose an oblique DLCQ as a limit to realize a theory of multiple M2-branes in M(atrix)-theory context. The limit is a combination of an infinite boosting of a space-like circle and a tuned tilting of the circle direction. We obtain a series of supergravity solutions describing various dual configurations including multiple M2-branes. For an infinite boosting along a circle wrapped obliquely around a rectangular torus, Seiberg's DLCQ limit distorts the torus modulus. In the context of supergravity, we show explicitly how this torus modulus of $\widetilde{\text M}$-theory is realized as the vacuum modulus of dual IIB-theory.Comment: v3: 25pages, extended version, References adde

Supersymmetric branes with (almost) arbitrary tensions

We present a supersymmetric version of the two-brane Randall-Sundrum scenario, with arbitrary brane tensions T_1 and T_2, subject to the bound |T_{1,2}| \leq \sqrt{-6\Lambda_5}, where \Lambda_5 < 0 is the bulk cosmological constant. Dimensional reduction gives N=1, D=4 supergravity, with cosmological constant \Lambda_4 in the range \half\Lambda_5 \leq \Lambda_4 \leq 0. The case with \Lambda_4 = 0 requires T_1 = -T_2 = \sqrt{-6\Lambda_5}. This work unifies and generalizes previous approaches to the supersymmetric Randall-Sundrum scenario. It also shows that the Randall-Sundrum fine-tuning is not a consequence of supersymmetry.Comment: 19pp; Published versio

The Number of States of Two Dimensional Critical String Theory

We discuss string theory vacua which have the wrong number of spacetime dimensions, and give a crude argument that vacua with more than four large dimensions are improbable. We then turn to two dimensional vacua, which naively appear to violate Bekenstein's entropy principle. A classical analysis shows that the naive perturbative counting of states is unjustified. All excited states of the system have strong coupling singularities which prevent us from concluding that they really exist. A speculative interpretation of the classical solutions suggests only a finite number of states will be found in regions bounded by a finite area. We also argue that the vacuum degeneracy of two dimensional classical string theory is removed in quantum mechanics. The system appears to be in a Kosterlitz-Thouless phase. This leads to the conclusion that it is also improbable to have only two large spacetime dimensions in string theory. However, we note that, unlike our argument for high dimensions, our conclusions about the ground state have neglected two dimensional quantum gravitational effects, and are at best incomplete.Comment: 12 pages, harvma

Brane-induced supersymmetry breaking

We study spontaneous supersymmetry breaking induced by brane-localized dynamics in five-dimensional supergravity compactified on S^1/Z_2. We consider a model with gravity in the bulk and matter localized on tensionless branes at the orbifold fixed points. We assume that the brane dynamics give rise to effective brane superpotentials that trigger the supersymmetry breaking. We analyze in detail the super-Higgs effect. We compute the full spectrum and show that the symmetry breaking is spontaneous but nonlocal in the fifth dimension. We demonstrate that the model can be interpreted as a new, non-trivial implementation of a coordinate-dependent Scherk-Schwarz compactification.Comment: 15 pages. v2: improved treatment of brane actions, relation with conventional Scherk-Schwarz mechanism clarified, version to be published in JHE

Gauge and Supersymmetric Invariance of a Boundary Bagger-Lambert-Gustavsson Theory

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 Wess-Zumino-Witten model, with the generators of the Lie algebra replaced by the generators of the Lie 3-algebra. The gauge and supersymmetry variations of the boundary theory will exactly cancel the boundary terms generated by the gauge and supersymmetric variations of the bulk theory.Comment: 15 pages, 0 figures, accepted for publication in JHE

Non-abelian D=11 Supermembrane

We obtain a U(M) action for supermembranes with central charges in the Light Cone Gauge (LCG). The theory realizes all of the symmetries and constraints of the supermembrane together with the invariance under a U(M) gauge group with M arbitrary. The worldvolume action has (LCG) N=8 supersymmetry and it corresponds to M parallel supermembranes minimally immersed on the target M9xT2 (MIM2). In order to ensure the invariance under the symmetries and to close the corresponding algebra, a star-product determined by the central charge condition is introduced. It is constructed with a nonconstant symplectic two-form where curvature terms are also present. The theory is in the strongly coupled gauge-gravity regime. At low energies, the theory enters in a decoupling limit and it is described by an ordinary N=8 SYM in the IR phase for any number of M2-branes.Comment: Contribution to the Proceedings of the Dubna International SQS'09 Workshop ("Supersymmetries and Quantum Symmetries-2009", July 29 - August 3, 2009. 12pg, Late