The heat kernel of the compactified supermembrane with non-trivial winding

Boulton, Lyonell; Restuccia, A.

doi:10.1016/j.nuclphysb.2005.07.004

Cited by 21 publications

(40 citation statements)

References 23 publications

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“…In this sense, it is a natural way to introduce monopole configurations which stabilizes the supermembrane. In fact, the resulting regularized Hamiltonian has a discrete spectrum , that is the essential spectrum is empty [28], [30], [31], [35]. The additional global structure we will consider involves in a manifest way the SL(2,Z) duality group of String theory.…”

Section: Introductionmentioning

confidence: 99%

SL(2, Z) symmetries, supermembranes and symplectic torus bundles

Moral

Martı́n

Peña

et al. 2011

J. High Energ. Phys.

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Section: Introductionmentioning

confidence: 99%

SL(2, Z) symmetries, supermembranes and symplectic torus bundles

Moral

Martı́n

Peña

et al. 2011

J. High Energ. Phys.

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“…The image of under this map is a calibrated submanifold of T 6 . The spectrum of the theory changes dramatically since it has a pure discrete spectrum at the classical and the quantum levels [38][39][40][41]43]; see also [42,45] 7 . The model that we study here involves additional symmetries beyond the original ones [41] which will be crucial in our coming discussion.…”

Section: M2 With Central Charges Associated With An Irreducible Windingmentioning

confidence: 99%

“…An independent proof was obtained in [43] using the spectral theorem and theorem 2 of that paper. In section 5 of [43], a rigorous proof of the Feynman formula for the Hamiltonian of the supermembrane was obtained.…”

Section: Quantum Properties Of the Supersymmetric Theorymentioning

confidence: 99%

A supermembrane with central charges on a G2 manifold

Belhaj¹,

Moral²,

Restuccia³

et al. 2009

J. Phys. A: Math. Theor.

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We construct an 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 with 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 discreteness of its supersymmetric spectrum. The corresponding 4D low energy effective field theory has N = 1 supersymmetry.

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“…Consequently it has a compact resolvent. We now use theorem 2 [22] to show that: i) The ghost and antighost contributions to the effective action assuming a gauge fixing condition linear on the configuration variables, ii) the fermionic contribution to the susy hamiltonian, do not change the qualitative properties of the spectrum of the hamiltonian.…”

Section: • the Supersymmetric Analysismentioning

confidence: 99%

Update on the quantum properties of the supermembrane

Moral

2009

Fortschritte der Physik

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In this note we summarize some of the quantum properties found since the early 80's until nowdays that characterize at quantum level the spectrum of the supermembrane. In particular we will focus on a topological sector of the 11D supermembrane that, contrary to the general case, has a purely discrete spectrum at supersymmetric level. This construction has been consistently implemented in different types of backgrounds: toroidal and orbifold-type with G2 structure able to lead to a true G2 compactification manifold. This theory has N = 1 supersymmetries in 4D. comment on the relevant points of this construction as well as on its spectral characteristics. We will also make some comments on the quantum properties of some effective formulation of multiple M2's theories recently found. The 11D supermembraneThe 11D supermembrane, also called M2 brane, [1] was discovered in 1987. A year later its hamiltonian formulation in the Light Cone Gauge (L.C.G.) and its matrix regularization by [3] was obtained. The supermembrane is the natural extension of the string in 11D and it was thought to be a fundamental object in 11D. However, the spectral properties of the regularized M2 differed substantially from those of the string as it was shown in a rigorous proof by [2]. Firstly, the theory of the supermembrane is a constrained system highly nonlinear and difficult to solve, in distinction with the harmonic oscillator-type hamiltonian of the string. Secondly, the supermembrane classically contains instabilities that make the scalar potential along directions in the configuration space vanish. They are called 'valleys' and render the classical system unstable. The third and most important difference is that its supersymmetric spectrum is continuous. Let us characterize it in more detail. The hamiltonian of the D = 11 Supermembrane [1] may be defined in terms of maps X μ , μ = 0, . . . , 10, from a base manifold Σ × R onto a target manifold which we will assume to be 11D Minkowski. Σ is a Riemann surface of genus g. σ a , a = 1, 2 are local spatial coordinates over Σ and τ ∈ R represents the worldvolume time. Decomposing X μ and Γ μ accordingly to the standard L.C.G ansatz and solving the constraints, the canonical reduced hamiltonian to the light-cone gauge has the expression

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The heat kernel of the compactified supermembrane with non-trivial winding

Cited by 21 publications

References 23 publications

SL(2, Z) symmetries, supermembranes and symplectic torus bundles

SL(2, Z) symmetries, supermembranes and symplectic torus bundles

A supermembrane with central charges on a G2 manifold

Update on the quantum properties of the supermembrane

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