The supermembrane with central charges: NCSYM, confinement and phase transition

Boulton, Lyonell; Moral, M. P. García del; Restuccia, A.

doi:10.1016/j.nuclphysb.2007.11.011

Cited by 14 publications

(45 citation statements)

References 47 publications

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“…Again as in the previous proofs, see the original argument in [25], ( b a ) is the inner product of two unitary vectors, hence ( b a ) 2 1. We assume there is a sequence ρ l , ϕ l such that P (ρ l , ϕ l ) → 0 then we must have…”

Section: Su(n ) Regularizationmentioning

confidence: 80%

See 1 more Smart Citation

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: Su(n ) Regularizationmentioning

confidence: 80%

“…On one hand the bosonic potential in the continuum [25] has the same type of quadratic lower bound as the regularized model. Moreover, there is a well-defined convergence of the regularized eigenvalues to the continuum theory eigenvalues in the semiclassical regime.…”

Section: Aims and Scopes Of The Present Papermentioning

confidence: 99%

Spectral properties in supersymmetric matrix models

Boulton¹,

Moral²,

Restuccia³

2012

Nuclear Physics B

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“…It is interesting that there are well-defined sectors of the supermembrane theory (with topological central charge different from zero) which have a discrete spectrum from (0, ∞) with isolated eigenvalues with finite multiplicity [25][26], [27]. We will show in this section that the scalar bosonic potentials for the M-branes, BLG, ABJM and ABJ theories, all have an associated Schröedinger operator with discrete spectrum from zero to infinity, with isolated eigenvalues which have finite multiplicity.…”

Section: Connection With Abjm-like Theoriesmentioning

confidence: 99%

“…There are several related toy models which also have continuous spectrum, see for example [20]. It is only when the supermembrane is restricted by certain topological conditions, non-trivial central charges, that the spectrum becomes discrete, with eigenvalues accumulating at infinity [23,24,25,26,27]. In order to analyse with more precision the supermembrane and super 5-brane potentials, and even more complicated potentials as in the BLG and ABJM theories it is very useful to consider a necessary and sufficient condition to have a discrete spectrum.…”

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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“…However, semiclassical analyses suggest that the spectrum of the model is indeed discrete [23,25,26,27]. In other words, quantum corrections lift the classical flat directions, and the quantum effective potential does indeed acquire a mass term.…”

Section: Introductionmentioning

confidence: 97%

Mass-Gaps and Spin Chains for (Super)membranes

Agarwal

2007

Int. J. Mod. Phys. A

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We present a method for computing the non-perturbative mass-gap in the theory of Bosonic membranes in flat background spacetimes. The analysis is extended to the study of membranes coupled to background fluxes as well. The computation of mass-gaps is carried out using a matrix regularization of the membrane Hamiltonians. The mass gap is shown to be naturally organized as an expansion in a 'hidden' parameter, which turns out to be 1 d : d being the related to the dimensionality of the background space. We then proceed to develop a large N perturbation theory for the membrane/matrix-model Hamiltonians around the quantum/mass corrected effective potential. The same parameter that controls the perturbation theory for the mass gap is also shown to control the Hamiltonian perturbation theory around the effective potential. The large N perturbation theory is then translated into the language of quantum spin chains and the one loop spectra of various Bosonic matrix models are computed by applying the Bethe ansatz to the one-loop effective Hamiltonians for membranes in flat space times. The spin chains corresponding to the large N effective Hamiltonians for the relevant matrix models are generically not integrable. However, we are able to find large integrable sub-sectors for all the spin chains of interest. Moreover, the continuum limits of the spin chains are mapped to integrable Landau-Lifschitz models even if the underlying spin chains are not integrable. Apart from membranes in flat spacetimes, the recently proposed matrix models (hep-th/0607005) for non-critical membranes in plane wave type spacetimes are also analyzed within the paradigm of quantum spin chains. The Bosonic sectors of all the models proposed in (hep-th/0607005) are diagonalized at the one-loop level and an intriguing connection between the existence of supersymmetric vacua and one-loop integrability is also presented.

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The supermembrane with central charges: NCSYM, confinement and phase transition

Cited by 14 publications

References 47 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

Mass-Gaps and Spin Chains for (Super)membranes

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