Supermembrane theory on a curved constant background

International Journal of Geometric Methods in Modern Physics, 2013

We show that the supermembrane theory compactified on a torus is invariant under T-duality. There are two different topological sectors of the compactified supermembrane (M2) classified according to a vanishing or nonvanishing second cohomology class. We find the explicit T-duality transformation that acts locally on the supermembrane theory and we show that it is an exact symmetry of the theory. We give a global interpretation of the T-duality in terms of bundles. It has a natural description in terms of the cohomology of the base manifold and the homology of the target torus. We show that in the limit when the torus degenerate into a circle and the M2 mass operator restricts to the string-like configurations, the usual closed string T-duality transformation between the type IIA and type IIB mass operators is recovered. Moreover, if we just restrict M2 mass operator to string-like configurations but we perform a generalized T-duality we find the SL(2,Z) nonperturbative multiplet of...

Journal of High Energy Physics

In this work we obtain classical solutions of the bosonic sector of the supermembrane theory with two-form fluxes associated to a quantized constant C± background. This theory satisfies a flux condition on the worldvolume that induces monopoles over it. Classically it is stable as it does not contain string-like spikes with zero energy in distinction with the general case. At quantum level the bosonic membrane has a purely discrete spectrum but the relevance is that the same property holds for its supersymmetric spectrum. We find for this theory spinning membrane solutions, some of them including the presence of a non-vanishing symplectic gauge connection defined on its worldvolume in different approximations. By using the duality found between this theory and the so-called supermembrane with central charges, rotating membrane solutions found in that case, are also solutions of the M2-brane with C± fluxes. We generalize this result to other embeddings. We find new distinctive rotati...

2021

In this work we obtain classical solutions of the bosonic sector of the supermembrane theory with two-form fluxes associated to a quantized constant C± background. This theory satisfies a flux condition on the worldvolume that induces monopoles over it. Classically it is stable as it does not contain string-like spikes with zero energy in distinction with the general case. At quantum level the bosonic membrane has a purely discrete spectrum but the relevance is that the same property holds for its supersymmetric spectrum. We find for this theory spinning membrane solutions, some of them including the presence of a non-vanishing symplectic gauge connection defined on its worldvolume in different approximations. By using the duality found between this theory and the so-called supermembrane with central charges, rotating membrane solutions found in that case, are also solutions of the M2-brane with C± fluxes. We generalize this result to other embeddings. We find new distinctive rotati...

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

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.

Physics Letters B, 2006

We discuss an open supermembrane in the presence of a constant three-form. The boundary conditions to ensure the κ-invariance of the action lead to possible Dirichlet branes. It is shown that a noncommutative (NC) M5-brane is possible as a boundary and the self-duality condition that the flux on the world-volume satisfies is derived from the requirement of the κ-symmetry. We also find that the open supermembrane can attach to each of infinitely many M2-branes on an M5-brane, namely a strong flux limit of the NC M5-brane.

Physics Letters B, 1997

The (q 1 , q 2) SL(2, Z) string bound states of type IIB superstring theory admit two inequivalent (T-dual) representations in eleven dimensions in terms of a fundamental 2-brane. In both cases, the spectrum of membrane oscillations can be determined exactly in the limit g 2 → ∞, where g 2 is the type IIA string coupling. We find that the BPS mass formulas agree, and reproduce the BPS mass spectrum of the (q 1 , q 2) string bound state. In the non-BPS sector, the respective mass formulas apply in different corners of the moduli space. The axiomatic requirement of T-duality in M-theory permits to derive a discrete mass spectrum in a (thin torus) region where standard supermembrane theory undergoes instabilities.

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.

Journal of Physics A: Mathematical and Theoretical, 2009

We construct the 11D supermembrane with topological central charges induced through an irreducible winding on a G2 manifold realized from the T 7 /Z 3 2 orbifold construction. The hamiltonian H of the theory on a T 7 target has a discrete spectrum. Within the discrete symmetries of H associated to large diffeomorphisms, the Z 2 ×Z 2 ×Z 2 group of automorphisms of the quaternionic subspaces preserving the octonionic structure is relevant. By performing the corresponding identification on the target space, the supermembrane may be formulated on a G2 manifold, preserving the discretness of its supersymmetric spectrum. The corresponding 4D low energy effective field theory has N = 1 supersymmetry.

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.

Progress of Theoretical Physics, 1997

We prove the Lorentz symmetry of supermembrane theory in the light cone gauge to complete the program initiated by de Wit, Marquard and Nicolai. We give some comments on extending the formulation to the M(atrix) 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...

Arxiv preprint hep-th/9809103, 1998

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. * [email protected] ;[email protected] † [email protected] ‡ [email protected]