Area-preserving diffeomorphisms and supermembrane Lorentz invariance

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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“…The U(N) regularization of the 11D supermembrane [3] was introduced in [4][5][6]. The resulting action is the so-called (1 + 0) SYM theory.…”

Section: Introductionmentioning

confidence: 99%

Spectral properties in supersymmetric matrix models

Boulton¹,

Moral²,

Restuccia³

2012

Nuclear Physics B

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“…For the BLG case a 3-algebra relation is satisfied (28) [ [33], [23]. We substitute the scalar potential by a regularized one…”

Section: Connection With Abjm-like Theoriesmentioning

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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“…Part of their study was based on a previous work on the area preserving diffeomorphisms in [8]. In [7] the hamiltonian of the theory was explicitly obtained.…”

Section: Introductionmentioning

confidence: 99%

“…It is their transformation law under the symmetry generated by the first class constraint. To analyze this point we introduce as in [8] the structure constants g…”

Section: Introductionmentioning

confidence: 99%

Spectrum of a noncommutative formulation of theD=11supermembrane with winding

Moral

Restuccia

2002

Phys. Rev. D

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A regularized model of the double compactified D=11 supermembrane with nontrivial winding in terms of SU(N) valued maps is obtained. The condition of nontrivial winding is described in terms of a nontrivial line bundle introduced in the formulation of the compactified supermembrane. The multivalued geometrical objects of the model related to the nontrivial wrapping are described in terms of a SU(N) geometrical object which in the N → ∞ limit, converges to the symplectic connection related to the area preserving diffeomorphisms of the recently obtained non-commutative description of the compactified D=11 supermembraneThe SU(N) regularized canonical lagrangian is explicitly obtained. In the N → ∞ limit it converges to the lagrangian in [1][2] subject to the nontrivial winding condition. The spectrum of the hamiltonian of the double compactified D=11 supermembrane is discussed. Generically, it contains local string like spikes with zero energy. However the sector of the theory corresponding to a principle bundle characterized by the winding number n = 0, described by the SU(N) model we propose, is shown to have no local string-like spikes and hence the spectrum of this sector should be discrete.

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Area-preserving diffeomorphisms and supermembrane Lorentz invariance

Cited by 99 publications

References 15 publications

Spectral properties in supersymmetric matrix models

Spectral properties in supersymmetric matrix models

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

Spectrum of a noncommutative formulation of theD=11supermembrane with winding

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