From supermembrane to matrix string

Annals of Physics, 1988

We study in detail the structure of the Lorentz covariant, spacetime supersymmetric lldimensional supermembrane theory. We show that for a flat spacetime background, the spacetime supersymmetry becomes an N =8 world volume (rigid) supersymmetry in a "physical" gauge; we also present the field equations and transformation rules in a "lightcone" gauge. We semiclassically quantize the closed torodial supermembrane on a spacetime (Minkowki),

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

Physics Letters B, 1997

We consider open supermembranes in an eleven dimensional background. We show that, in a flat space-time, the world-volume action is kappa-symmetric and has global space-time supersymmetry if space-time has even dimensional topological defects where the membrane can end. An example of such topological defects is provided by the space-time with boundaries considered by Horava and Witten. In that case the world-volume action has reparametrisation anomalies whose cancellation requires the inclusion of a current algebra on the boundaries of the membrane. The role of kappa-anomalies in a general background is discussed. The tension of the membrane is related to the eleven dimensional gravitational constant with the aid of the Green-Schwarz mechanism allowing a consistency check of M-theory.

Nuclear Physics B, 1997

The supermembrane theory on R 10 ×S 1 is investigated, for membranes that wrap once around the compact dimension. The Hamiltonian can be organized as describing N s interacting strings, the exact supermembrane corresponding to N s → ∞. The zero-mode part of N s − 1 strings turn out to be precisely the modes which are responsible of instabilities. For sufficiently large compactification radius R 0 , interactions are negligible and the lowest-energy excitations are described by a set of harmonic oscillators. We compute the physical spectrum to leading order, which becomes exact in the limit g 2 → ∞, where g 2 ≡ 4π 2 T 3 R 3 0 and T 3 is the membrane tension. As the radius is decreased, more strings become strongly interacting and their oscillation modes get frozen. In the zero-radius limit, the spectrum is constituted of the type IIA superstring spectrum, plus an infinite number of extra states associated with flat directions of the quartic potential.

Modern Physics Letters A, 1996

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 Mbrane is related to the maximally extended supersymmetry implied by the 'Lorentz' covariance and dimensional reasons. The Kähler-Chern-Simons-type action describing the self-dual gravity in 2 + 2 dimensions is proposed. Its maximal supersymmetric extension (of the Green-Schwarz-type) naturally leads to the 2 + 10 (or higher) dimensions for the M-brane target space. The proposed OSp(32|1) supersymmetric action gives the pre-geometrical description of M-branes, which may be useful for a fundamental formulation of F&M theory.

Journal of High Energy Physics, 2021

We obtain the Hamiltonian formulation of the 11D Supermembrane theory non-trivially compactified on a twice punctured torus times a 9D Minkowski space-time. It corresponds to a M2-brane formulated in 11D space with ten non-compact dimensions. The critical points like the poles and the zeros of the fields describing the embedding of the Supermembrane in the target space are treated rigorously. The non-trivial compactification generates non-trivial mass terms appearing in the bosonic potential, which dominate the full supersymmetric potential and should render the spectrum of the (regularized) Supermembrane discrete with finite multiplicity. The behaviour of the fields around the punctures generates a cosmological term in the Hamiltonian of the theory.The massive supermembrane can also be seen as a nontrivial uplift of a supermembrane torus bundle with parabolic monodromy in M9 × T2. The moduli of the theory is the one associated with the punctured torus, hence it keeps all the nontri...

1996

We present an approach to membrane quantization using matrix quantum mechanics at large N. We show that this leads (through a simple field theory of two-dimensional open strings and the associated SU(\infty) current algebra) to a 4-D dynamics of self-dual gravity plus matter.

2003

We discuss an open supermembrane theory in the AdS4×S and AdS7×S backgrounds. The possible Dirichlet branes of an open supermembrane are classified by analyzing the covariant Wess-Zumino term. All of the allowed configurations are related to those on the pp-wave background via the Penrose limit.

Journal of High Energy Physics, 2009

While string or Yang-Mills theories are based on Lie algebra or two-algebra structure, recent studies indicate that M-theory may require a one higher, three-algebra structure. Here we construct a covariant action for a supermembrane in eleven dimensions, which is invariant under global supersymmetry, local fermionic symmetry and worldvolume diffeomorphism. Our action is classically on-shell equivalent to the celebrated Bergshoeff-Sezgin-Townsend action. However, the novelty is that we spell the action genuinely in terms of Nambu three-brackets: All the derivatives appear through Nambu brackets and hence it manifests the three-algebra structure. Further the double dimensional reduction of our action gives straightforwardly to a type IIA string action featuring two-algebra. Applying the same method, we also construct a covariant action for type IIB superstring, leading directly to the IKKT matrix model.

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.