Jerome P. Gauntlett, Jan B. Gutowski
We study the recent construction of maximally supersymmetric field theory Lagrangians in three spacetime dimensions that are based on algebras with a triple product. Assuming that the algebra has a positive definite metric compatible with the triple product, we prove that the only non-trivial examples are either the well known case based on a four dimensional algebra or direct sums thereof.
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We write down a maximally supersymmetric one parameter deformation of the field theory action of Bagger and Lambert. We show that this theory on RxT^2 is invariant under the superalgebra of the maximally supersymmetric Type IIB plane wave. It is argued that this theory holographically describes the Type IIB plane wave in the discrete light-cone quantization (DLCQ).
We solve the superspace Bianchi identities for ten-dimensional supersymmetric Yang-Mills theory without imposing any kind of constraints apart from the standard conventional one. In this way we obtain a set of algebraic conditions on certain fields which in the on-shell theory are constructed as composite ones out of the physical fields. These conditions must hence be satisfied by any kind of theory in ten dimensions invariant under supersymmetry and some, abelian or non-abelian, gauge symmetry. Deformations of the ordinary SYM theory (as well as the fields) are identified as elements of a cer…
We look into the general aspects of space-time symmetries in presence of torsion, and how the latter is affected by such symmetries. Focusing in particular to space-times which either exhibit maximal symmetry on their own, or could be decomposed to maximally symmetric subspaces, we work out the constraints on torsion in two different theoretical schemes. We show that at least for a completely antisymmetric torsion tensor (for e.g. the one motivated from string theory), an equivalence is set between these two schemes, as the non-vanishing independent torsion tensor components turn out to be the…
We consider supermembranes in the maximally supersymmetric plane wave geometry of the eleven dimensions and construct complete solutions of the continuum version of the 1/4 BPS equations. The supermembranes may have an arbitrary number of holes and arbitrary cross sectional shapes. In the matrix regularized version, we solve the matrix equations for several simple cases including fuzzy torus. In addition, we show that these solutions are trivially generalized to 1/8 and 1/16 BPS configuations.
In 1980, Antonio Aurilia, Hermann Nicolai and I constructed an N=8 supergravity with a positive exponential potential for one of the 70 scalar fields by adapting the dimensional reduction of 11D supergravity to allow for a non-zero 4-form field-strength in 4D. This model, now viewed as a particular gauged maximal supergravity, had little influence at the time because it does not have a maximally-symmetric vacuum. However, as shown here, it does have a domain-wall solution, which lifts to the M2-brane solution of D=11 supergravity. The possibility of a similar construction for other branes of M…
We compare the bosonic and maximally supersymmetric membrane models. We find that in Hoppe regulated form the bosonic membrane is well approximated by massive Gaussian quantum matrix models. In contrast the similarly regulated supersymmetric membrane, which is equivalent to the BFSS model, has a gravity dual description. We sketch recent progress in checking gauge/gravity duality in this context.
We study a spherical antimembrane in the eleven dimensional pp wave. In this background, a single antimembrane breaks all the supersymmetries because its dipole is misaligned with the background flux. Using the BMN matrix theory we compute the one-loop potential for the antimembrane. Then we put the antimembrane in the field produced by a source spherical membrane and compute the velocity-dependent part of the interaction between them on both the supergravity side and the BMN matrix theory side. Despite the aforementioned nonsupersymmetry of the antimembrane, it is found that the results on th…
We find M-theory solutions that are holographic duals of flows of the maximally supersymmetric N=8 scalar-fermion theory in (2+1) dimensions. In particular, we construct the M-theory solution dual to a flow in which a single chiral multiplet is given a mass, and the theory goes to a new infra-red fixed point. We also examine this new solution using M2-brane probes. The (2+1)-dimensional field theory fixed-point is closely related to that of Leigh and Strassler, while the M-theory solution is closely related to the corresponding IIB flow solution. We recast the IIB flow solution in a more geome…
We review developments in the theory of multiple, parallel membranes in M-theory. After discussing the inherent difficulties pertaining to a maximally supersymmetric lagrangian formulation with the appropriate field content and symmetries, we discuss how introducing the concept of 3-algebras allows for such a description. Different choices of 3-algebras lead to distinct classes of 2+1 dimensional theories with varying degrees of supersymmetry. We then describe how these are equivalent to a type of conventional superconformal Chern-Simons gauge theories at level k, coupled to bifundamental matt…
We study the closed and open supermembranes on the maximally supersymmetric pp-wave background. In the framework of the membrane theory, the superalgebra is calculated by using the Dirac bracket and we obtain its central extension by surface terms. The result supports the existence of the extended objects in the membrane theory in the pp-wave limit. When the central terms are discarded, the associated algebra completely agrees with that of Berenstein-Maldacena-Nastase matrix model. We also discuss the open supermembranes on the pp-wave and elaborate the possible boundary conditions.
Supersymmetric $σ$-models obtained by constraining linear supersymmetric field theories are ill defined. Well defined subsectors parametrising Kahler manifolds exist but are not believed to arise directly from constrained linear ones. A counterexample is offered using improved understanding of membranes in superstring theories leading to crucial central terms modifying the algebra of supercharge densities
Based on the recently proposed action for Matrix theory describing the DLCQ M theory in the maximally supersymmetric pp-wave background, we obtain the supersymmetry algebra of supercharge density. Using supersymmetry transformation rules for fermions, we identify BPS states with the central charges in the supersymmetry algebra, which can be activated only in the large N limit. They preserve some fraction of supersymmetries and correspond to rotating transverse membranes and longitudinal five branes.
Our goal is to study the supermembrane on an $AdS_4 \times \cal M_7$ background, where $\cal M_7$ is a 7--dimensional Einstein manifold with $N$ Killing spinors. This is a direct way to derive the $Osp(N|4)$ singleton field theory with all the additional properties inherited from the geometry of the internal manifold. As a first example we consider the maximally supersymmetric $Osp(8|4)$ singleton corresponding to the choice $\cal M_7 = S^7$. We find the explicit form of the action of the membrane coupled to this background geometry and show its invariance under non--linearly realised supercon…
Taking the (2,2) strings as a starting point, we discuss the equivalent integrable field theories and analyze their symmetry structure in 2+2 dimensions from the viewpoint of string/membrane unification. Requiring the Lorentz invariance and supersymmetry in the (2,2) string target space leads to an extension of the (2,2) string theory to a theory of 2+2 dimensional supermembranes (M-branes) propagating in a higher dimensional target space. The origin of the hidden target space dimensions of the M-brane is related to the maximally extended supersymmetry implied by the Lorentz covariance and dim…
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