Properties of the eleven-dimensional supermembrane theory

Physics Letters B, 1998

We consider open supermembranes in eleven dimensions in the presence of closed M-Theory five-branes. It has been shown that, in a flat space-time, the worldvolume action is kappa invariant and preserves a fraction of the eleven dimensional supersymmetries if the boundaries of the membranes lie on the five-branes. We calculate the reparametrisation anomalies due to the chiral fermions on the boundaries of the membrane and examine their cancellation mechanism. We show that these anomalies cancel with the aid of a classical term in the world-volume action, provided that the tensions of the five-brane and the membrane are related to the eleven dimensional gravitational constant in a way already noticed in M-Theory. 1

Physical Review D, 2001

We present a superspace formulation of N = 1 eleven-dimensional supergravity with no manifest local Lorentz covariance, which we call teleparallel superspace. This formulation will be of great importance, when we deal with other supergravity theories in dimensions higher than eleven dimensions, or a possible formulation of noncommutative supergravity. As an illustrative example, we apply our teleparallel superspace formulation to the case of N = 1 supergravity in twelve-dimensions. We also show the advantage of teleparallel superspace as backgrounds for supermembrane action.

Nuclear Physics B, 2006

We classify the supersymmetric mass deformations of all the super Yang-Mills quantum mechanics, which are obtained by dimensional reductions of minimal super Yang-Mills in spacetime dimensions: ten, six, four, three and two. The resulting actions can be viewed as the matrix descriptions of supermembranes in nontrivial backgrounds of one higher dimensional supergravity theories. We also discuss the utmost generalization of the light-cone formulation of the Nambu-Goto action for a p-brane, including time dependent backgrounds.

Physical Review D, 2001

It is shown that a double compactified D = 11 supermembrane with non trivial wrapping may be formulated as a symplectic non-commutative gauge theory on the world volume. The symplectic non commutative structure is intrinsically obtained from the symplectic 2-form on the world volume defined by the minimal configuration of its hamiltonian. The gauge transformations on the symplectic fibration are generated by the area preserving diffeomorphisms on the world volume. Geometrically, this gauge theory corresponds to a symplectic fibration over a compact Riemman surface with a symplectic connection. * isbeliam@usb.ve ;isbeliam@ic.ac.uk † jovalle@usb.ve ‡ arestu@usb.ve

Physics Letters B, 1996

The usual supermembrane solution of D = 11 supergravity interpolates between R 11 and AdS 4 × round S 7 , has symmetry P 3 × SO(8) and preserves 1/2 of the spacetime supersymmetries for either orientation of the round S 7 . Here we show that more general supermembrane solutions may be obtained by replacing the round S 7 by any seven-dimensional Einstein space M 7 . These have symmetry P 3 × G, where G is the isometry group of M 7 . For example, G = SO(5) × SO(3) for the squashed S 7 . For one orientation of M 7 , they preserve N/16 spacetime supersymmetries where 1 ≤ N ≤ 8 is the number of Killing spinors on M 7 ; for the opposite orientation they preserve no supersymmetries since then M 7 has no Killing spinors. For example N = 1 for the left-squashed S 7 owing to its G 2 Weyl holonomy, whereas N = 0 for the right-squashed S 7 . All these solutions saturate the same Bogomol'nyi bound between the mass and charge. Similar replacements of S D−p−2 by Einstein spaces M D−p−2 yield new super p-brane solutions in other spacetime dimensions D ≤ 11. In particular, simultaneous dimensional reduction of the above D = 11 supermembranes on S 1 leads to a new class of D = 10 elementary string solutions which also have fewer supersymmetries.

Physics Letters B, 1999

This is a short note on the relation of the Matrix model with the non-commutative geometry of the 11-dimensional supermembrane. We put forward the idea that Mtheory is described by the t' Hooft topological expansion of the Matrix model in the large N-limit where all topologies of membranes appear. This expansion can faithfully be represented by the Moyal Yang-Mills theory of membranes. We discuss this conjecture in the case of finite N, where the non-commutative geometry of the membrane is given be the finite quantum mechanics. The use of the finite dimensional representations of the Heisenberg group reveals the cellular structure of a toroidal supemembrane on which the Matrix model appears as a non-commutatutive Yang-Mills theory. The Moyal star product on the space of functions in the case of rational values of Planck constant represents exactly this cellular structure. We also discuss the integrability of the instanton sector as well as the topological charge and the corresponding Bogomol'nyi bound.

Arxiv preprint hep-th/9809103, 1998

Physical Review D, 1998

We study open supermembranes in 11 dimensional rigid superspace with 6 dimensional topological defects (M-theory five-branes). After rederiving in the Green-Schwarz formalism the boundary conditions for open superstrings in the type IIA theory, we determine the boundary conditions for open supermembranes by imposing kappa symmetry and invariance under a fraction of 11 dimensional supersymmetry. The result seems to imply the self-duality of the three-form field strength on the fivebrane world volume. We show that the light-cone gauge formulation is regularized by a dimensional reduction of a 6 dimensional N=1 super Yang-Mills theory with the gauge group SO(N→ ∞). We also analyze the SUSY algebra and BPS states in the light-cone gauge.

Physics Letters B, 2000

We present a Lorentz invariant lagrangian formulation for a supersymmetric Yang-Mills vector multiplet in eleven dimensions (11D). The Lorentz symmetry is broken at the field equation level, and therefore the breaking is spontaneous, as in other formulations of supersymmetric theories in 12D or higher dimensions. We introduce a space-like unit vector formed by the gradient of a scalar field, avoiding the problem of Lorentz non-invariance at the lagrangian level, which is also an analog of non-commutative geometry with constant field strengths breaking Lorentz covariance. The constancy of the space-like unit vector field is implied by the field equation of a multiplier field. The field equations for the physical fields are formally the same as those of 10D supersymmetric Yang-Mills multiplet, but now with some constraints on these fields for supersymmetric consistency. This formulation also utilizes the multiplier fields accompanied by the bilinear forms of constraints, such that these multiplier fields will not interfere with the physical field equations. Based on this component result, we also present a κ-symmetric supermembrane action with the supersymmetric Yang-Mills backgrounds.

2002

The issue of justifying the matrix-theory proposal is revisited. We first discuss how the matrix-string theory is derived directly starting from the eleven dimensional supermembrane wrapped around a circle of radius R = g s ℓ s , without invoking any stringy assumptions, such as Sand T-dualities. This derivation provides us a basis for studying both string (R → 0)-and M (R → ∞)-theory limits of quantum membrane theory in a single unified framework. In particular, we show that two different boosts of supermembrane, namely one of unwrapped membrane along the M-theory circle and the other of membrane wrapped about a transervse direction which is orthogonal to the M-theory circle, give the same matrix theory in the 11 dimensional limit, R → ∞ (with N → ∞). We also discuss briefly the nature of possible covariantized matrix (string) theories.