Open supermembranes in eleven dimensions

Arxiv preprint arXiv:1012.2707, 2010

This thesis consists of two parts. In the first part we investigate the worldvolume supersymmetry algebra of multiple membrane theories. We begin with a description of M-theory branes and their intersections from the perspective of spacetime and worldvolume supersymmetry algebras. We then provide an overview of the recent work on multiple M2-branes focusing on the Bagger-Lambert theory and its relation to the Nambu-Poisson M5-brane and the ABJM theory. The worldvolume supersymmetry algebras of these theories are explicitly calculated and the charges interpreted in terms of spacetime intersections of M-branes. The second part of the thesis looks at l 3 p corrections to the supersymmetry transformations of the Bagger-Lambert theory. We begin with a review of the dNS duality transformation which allows a gauge field to be dualised to a scalar field in 2+1 dimensions. Applying this duality to α ′2 terms of the non-abelian D2-brane theory gives rise to the l 3 p corrections of the Lorentzian Bagger-Lambert theory. We then apply this duality transformation to the α ′2 corrections of the D2-brane supersymmetry transformations. For the 'abelian' Bagger-Lambert theory we are able to uniquely determine the l 3 p corrections to the supersymmetry transformations of the scalar and fermion fields. Generalising to the 'non-abelian' Bagger-Lambert theory we are able to determine the l 3 p correction to the supersymmetry transformation of the fermion field. Along the way make a number of observations relating to the implementation of the dNS duality transformation at the level of supersymmetry transformations.

2018

In this work we obtain the Hamiltonian description of the Supermembrane theory formulated in the Light Cone Gauge (L.C.G.) on M_9× T^2 background with constant bosonic three-forms C_± ab. We analyze three different cases depending on the particular values of the constants (C_+ab,C_-ab). When it is imposed a 2-form flux condition over C_+ and vanishing C_-, it coincides with the Halmiltonian of a supermembrane theory irreducibly wrapped around the 2-torus with a vanishing three-form C_μνρ=0, shifted by a constant term. The 2-torus target space flux condition of the first theory induces by a pullback a worldvolume flux that can be identified with the topological invariant associated to the irreducibility of the wrapping condition that appears in the second theory considered. Both theories exhibit a nonvanishing central charge condition in the algebra. The M2-brane theory with constant C_+ exhibits discreteness of the supersymetric spectrum as the theory of irreducible wrapping does, i...

Physics Letters B, 1989

We construct new vacua for the eleven-dimensional supermembrane in which spacetime is the product of four-dimensional anti-de Sitter space and a compact seven-dimensional Einstein space, and the membrane is a sphere of non-zero radius in the anti-de Sitter space. In one class of solution the radius is a specific multiple of the anti-de Sitter scale parameter while in a second class the radius is arbitrary. Remarkably, only two of the Freund-Rubin compactifications admit vacua of the latter class: the round seven-sphere with N=8 supersymmetry and the N(0, 1) space with N=3 supersymmetry.

European Physical Journal C, 1999

We suggest that the static configurations of M-theory may be described by the matrix regularization of the supermembrane theory in static regime. We compute the long-range interaction between a M2-brane and an anti-M2-brane in agreement with the 11-dimensional supergravity result.

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 supermem- brane wrapped around a circle of radius R = gsℓs, without invoking any stringy assump- tions, such as S- and 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.

Nucl Phys B, 2002

Through direct examination of the effect of the OM limit on the M2-brane worldvolume action, we derive a membrane action for OM theory, and more generally, for the eleven-dimensional M-theoretic construct known as Galilean or Wrapped M2-brane (WM2) theory, which contains OM theory as a special class of states. In the static gauge, the action in question implies a discrete spectrum for the closed membrane of WM2 theory, which under double dimensional reduction is shown to reproduce the known NCOS/Wound closed string spectrum. We examine as well open membranes ending on each of the three types of M5-branes in WM2 theory (OM theory arising from the 'longitudinal' type), and show that the 'fully transverse' fivebrane is tensionless. As a prelude to the membrane, we also study the case of the string, where we likewise obtain a reparametrization-invariant action, and make contact with previous work.

Nuclear Physics B, 1999

Our goal is to study the supermembrane on an AdS 4 × M 7 background, where 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 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 realized superconformal transformations. To do this we introduce the supergroup generalization of the solvable Lie algebra parametrization of non-compact coset spaces. We also derive the action of quantum fluctuations around the classical configuration, showing that this is precisely the singleton action. We find that the singleton is simply realized as a free field theory living on flat Minkowski space.

Journal of High Energy Physics, 2008

The action of the 11D supermembrane with nontrivial central charges compactified on a 7D toroidal manifold is obtained. It describes a supermembrane evolving in a 4d Minkowski space-time. The action is invariant under additional symmetries in comparison to the supermembrane on a Minkowski target space. The hamiltonian in the LCG is invariant under conformal transformations on the Riemann surface base manifold. The spectrum of the regularized hamiltonian is discrete with finite multiplicity. Its resolvent is compact. Susy is spontaneously broken, due to the topological central charge condition, to four supersymmetries in 4D, the vacuum belongs to an N=1 supermultiplet. When assuming the target-space to be an isotropic 7-tori, the potential does not contain any flat direction, it is stable on the moduli space of parameters.

Arxiv preprint hep-th/9809103, 1998

Physics Letters B, 1998

In this letter we discuss the supersymmetry issue of the self-dual supermembranes in (8 + 1) and (4 + 1)-dimensions. We nd that all genuine solutions of the (8 + 1)dimensional supermembrane, based on the exceptional group G 2 , preserve one of the sixteen supersymmetries while all solutions in (4 + 1)-dimensions preserve eight of them.