The discrete spectrum of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mn>11</mml:mn></mml:math> bosonic M5-brane

Martı́n, I.; Navarro, L.; Pérez, Alejandro; Restuccia, A.

doi:10.1016/j.nuclphysb.2007.11.012

Cited by 6 publications

(4 citation statements)

References 20 publications

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“…The (1 + 0) SYM action was first obtained in [9][10][11] in the context of supersymmetric quantum models unrelated to M-theory. For other nonperturbative bosonic spectral analysis of inside the context of regularized p-branes see [12] for the M5-brane case and [13] for the regularized ABJ/M constructions for Super Chern-Simons-Matter theories.…”

Section: Introductionmentioning

confidence: 99%

Spectral properties in supersymmetric matrix models

Boulton¹,

Moral²,

Restuccia³

2012

Nuclear Physics B

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We formulate a general sufficiency criterion for discreteness of the spectrum of both supersymmmetric and non-supersymmetric theories with a fermionic contribution. This criterion allows an analysis of Hamiltonians in complete form rather than just their semiclassical limits. In such a framework we examine spectral properties of various (1 + 0) matrix models. We consider the BMN model of M-theory compactified on a maximally supersymmetric pp-wave background, different regularizations of the supermembrane with central charges and a non-supersymmetric model comprising a bound state of N D2 with m D0. While the first two examples have a purely discrete spectrum, the latter has a continuous spectrum with a lower end given in terms of the monopole charge. Crown

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Section: Introductionmentioning

confidence: 99%

Spectral properties in supersymmetric matrix models

Boulton¹,

Moral²,

Restuccia³

2012

Nuclear Physics B

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“…The discreteness of the spectrum of the bosonic M5 brane [24] has been characterized following the necessary and sufficiency condition showed in Sect. 1 [6].…”

Section: • Comments On the Multiple M2's Spectrummentioning

confidence: 99%

“…. , N, K ≥ L, N ≥ L, X = X a M ∈ R KN and f b a1...aL is a non-singular constant tensor totally antisymmetric and it is not www.fp-journal.org singular, then the spectrum of the bosonic hamiltonian is discrete [24]. This condition also holds for the type of bosonic scalar potentials of the multiple M2's actions based on 3-algebras (whenever a proper discretization is provided).…”

Section: • Comments On the Multiple M2's Spectrummentioning

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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“…An analysis of the spectrum of the D = 11, 5-brane in the light cone gauge, using the Molchanov, Maz'ya and Schubin theorem was performed in [30], [31]. The spectrum of the hamiltonian is also discrete.…”

Section: Introductionmentioning

confidence: 99%

Spectral analysis of polynomial potentials and its relation with ABJ/M-type theories

et al. 2010

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Abstract. We obtain a general class of polynomial potentials for which the Schröedinger operator has a discrete spectrum. This class includes all the scalar potentials in membrane, 5-brane, p-branes, multiple M2 branes, BLG and ABJM theories. We provide a proof of the discreteness of the spectrum of the associated Schröedinger operators. This a a first step in order to analyze BLG and ABJM supersymmetric theories from a non-perturbative point of view.

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The discrete spectrum of the D=11 bosonic M5-brane

Cited by 6 publications

References 20 publications

Spectral properties in supersymmetric matrix models

Spectral properties in supersymmetric matrix models

Update on the quantum properties of the supermembrane

Spectral analysis of polynomial potentials and its relation with ABJ/M-type theories

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