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Register a new userMass operator of the M2-brane on a background with constant three-form
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The formulation of supermembrane theory on nontrivial backgrounds is discussed. In particular, we obtain the Hamiltonian of the supermembrane on a background with constant bosonic three form on a target space $M_9 times T^2$.
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We describe a compactified Supermembrane, or M2-brane, with 2-form fluxes generated by constant three-forms that are turned on a 2-torus of the target space $M_9times T^2$. We compare this theory with the one describing a $11D$ M2-brane formulated on $M_9times T^2$ target space subject to an irreducible wrapping condition. We show that the flux generated by the bosonic 3-form under consideration is in a one to one correspondence to the irreducible wrapping condition. After a canonical transformation both Hamiltonians are exactly the same up to a constant shift in one particular case. Consequently both of them, share the same spectral properties. We conclude that the Hamiltonian of the M2-brane with 2-form target space fluxes on a torus has a purely discrete spectrum with eigenvalues of finite multiplicity and it can be considered to describe a new sector of the microscopic degrees of freedom of M-theory. We also show that the total membrane momentum in the direction associated to the flux condition acquires a quantized contribution in correspondence to the flux units that have been turned on.
We compute the large N limit of Wilson loop expectation values for a broad class of N=2 supersymmetric gauge theories defined on a general class of background three-manifolds M_3, diffeomorphic to S^3. We find a simple closed formula which depends on the background geometry only through a certain supersymmetric Killing vector field. The supergravity dual of such a Wilson loop is an M2-brane wrapping the M-theory circle, together with a complex curve in a self-dual Einstein manifold M_4, whose conformal boundary is M_3. We show that the regularized action of this M2-brane also depends only on the supersymmetric Killing vector, precisely reproducing the large N field theory computation.
We present the formulation of the bosonic Hamiltonian M2-brane compactified on a twice punctured torus following the procedure proposed in cite{mpgm14}. In this work we analyse two possible metric choice, different from the one used in cite{mpgm14}, over the target space and study some of the properties of the corresponding Hamiltonian.
We investigate the gauge/gravity duality between the ${cal N} = 6$ mass-deformed ABJ theory with U$_k(N+l)times$U$_{-k}(N)$ gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(2,1)$times$SO(4)/${mathbb Z}_ktimes$SO(4)/${mathbb Z}_k$ isometry and the discrete torsion $l$. For chiral primary operators with conformal dimensions $Delta=1,2$, we obtain the exact vacuum expectation values using the holographic method in 11-dimensional supergravity and show that the results depend on the shapes of droplet pictures in LLM geometries. The $frac{l}{sqrt{N}}$ contributions from the discrete torsion $l$ for several simple droplet pictures in the large $N$ limit are determined in holographic vacuum expectation values. We also explore the effects of the orbifolding ${mathbb Z}_k$ and the asymptotic discrete torsion $l$, on the gauge/gravity duality dictionary and on the nature of the asymptotic limits of the LLM geometries.
Supermembrane compactified on a $M_9times T^2$ target space is globally described by the inequivalent classes of torus bundles over torus. These torus bundles have monodromy in $SL(2,Z)$ when they correspond to the nontrivial central charge sector and they are trivial otherwise. The first ones contain eight inequivalent classes of M2-brane bundles which at low energies, are in correspondence with the eight type II gauged supergravities in $9D$. The relation among them is completely determined by the global action of T-duality which interchanges topological invariants of the two tori. The M2-brane torus bundles are invariant under $SL(2,Z)times SL(2,Z) times Z_2$. From the effective point of view, there is another dual invariant theory, called Double Field Theory which describe invariant actions under $O(D,D)$. Globally it is formulated in terms of doubled $2D$ torus fibrations over the spacetime with a monodromy given by $O(D,D,Z)$. In this note we discuss T-duality global aspects considered in both theories and we emphasize certain similarities between both approaches which could give some hints towards a deeper relationship between them.
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