The ground state of the D = 11 supermembrane and matrix models on compact regions

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

doi:10.1016/j.nuclphysb.2016.07.025

Cited by 8 publications

(17 citation statements)

References 43 publications

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“…Due to its complexity, a natural approach for the solution of this problem is to divide it into three parts, [5,4,6]. Firstly, determine the existence and uniqueness of a solution for the Dirichlet problem on a bounded region of arbitrary radius.…”

Section: Introductionmentioning

confidence: 99%

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Measure of the potential valleys of the supermembrane theory

2019

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We analyse the measure of the regularized matrix model of the supersymmetric potential valleys, Ω, of the Hamiltonian of non zero modes of supermembrane theory. This is the same as the Hamiltonian of the BFSS matrix model. We find sufficient conditions for this measure to be finite, in terms the spacetime dimension. For SU (2) we show that the measure of Ω is finite for the regularized supermembrane matrix model when the transverse dimensions in the light cone gauge D ≥ 5. This covers the important case of seven and eleven dimensional supermembrane theories, and implies the compact embedding of the Sobolev space H 1,2 (Ω) onto L 2 (Ω). The latter is a main step towards the confirmation of the existence and uniqueness of ground state solutions of the outer Dirichlet problem for the Hamiltonian of the SU (N ) regularized D = 11 supermembrane, and might eventually allow patching with the inner solutions.

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Section: Introductionmentioning

confidence: 99%

“…The overall state will then be the ground state of the Hamiltonian of the non-zero modes of the D = 11 supermembrane. In [6] (also [5,4]) we settled the first step. The present work is about the second step.…”

Section: Introductionmentioning

confidence: 99%

Measure of the potential valleys of the supermembrane theory

2019

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“…The algebra of the monodromy groups elliptic and hyperbolic with the U-duality transformation form a non-abelian algebra A(1) that acts like an scaling and a translation. The dual M2-brane bundle with these two inequivalent classes of monodromies corresponds to a single class of dual M2-brane bundles that we call A (1). At low energies we consider that it could be related it to the type IIA A(1) gauged supergravity in 9D.…”

Section: Discussionmentioning

confidence: 99%

“…Supermembranes are 2 + 1 dimensional objects embedded in 11D space-time that act as sources for D = 11 Supergravity and as a consequence of it there is a deep relation between both theories: on one hand Supermembrane theory is conjectured to contain a unique massless groundstate associated to the 11D supergravity multiplet. Several works have been developed in support of this claim, for a recent new approach see [1] and references therein. On the other, Supermembrane theories are expected to be described by supergravities at 'low energies'.…”

Section: Introductionmentioning

confidence: 90%

Classification of M2-brane 2-torus bundles, U -duality invariance, and type II gauged supergravities

2019

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In this paper we obtain the complete classification of the inequivalent classes of M2-brane symplectic torus bundles with monodromy in SL(2, Z) and their precise U-duality relations among them. There are eight inequivalent classes of bundles whose monodromy groups, at low energies, are in correspondence with the gauging groups of the eight type II gauged supergravities in nine dimensions. Four of those have been previously found and they correspond to the 'type IIB side'. In this paper we provide the explicit realization of the remaining four classes associated to the 'type IIA side'. The precise M2-brane U-duality relations between the eight inequivalent classes of bundles have allowed to identified the remaining four ones. We conjecture that the classes of gaugings -classifying the eight types of II gauged supergravity in nine dimensions-are determined by the inequivalent coinvariant classes associated to the base and the fiber of the supermembrane bundles and their duals.

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“…Despite a number of profound results concerning zero energy eigenfunctions, e.g. an explicit construction in the pure fermionic sector for the n = 2 model [22], large x behaviour [23], or existence results on compact regions [24], the question posed in the full generality remains open. We believe that the approach discussed in this paper can shed new light on this problem since our results correspond to the purely bosonic sector of the supermembrane and our construction can be possibly extended to the fermionic sectors allowing to study the embedded part of the spectrum of the supermembrane.…”

Section: Introductionmentioning

confidence: 99%

Optimized Fock space in the large N limit of quartic interactions in matrix models

Hynek

2016

Nuclear Physics B

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We consider the problem of quantization of the bosonic membrane via the large N limit of its matrix regularizations H N in Fock space. We prove that there exists a choice of the Fock space frequency such that H N can be written as a sum of a non-interacting Hamiltonian H 0,N and the original normal ordered quartic potential. Using this decomposition we obtain upper and lower bounds for the ground state energy in the planar limit, we study a perturbative expansion about the spectrum of H 0,N , and show that the spectral gap remains finite at N = ∞ at least up to the second order. We also apply the method to the U (N )-invariant anharmonic oscillator, and demonstrate that our bounds agree with the exact result of Brezin et al. * mkhynek@kth.se 1 See [6] for a discussion of the spectrum, including the supersymmetric version of the model and related issues 2 The power of n for a quartic interaction it is usually argued to be −1, (the t' Hooft coupling [8]), however note that due to the definition of f (n) abc which contains an explicit factor of n 3 2 , the coupling constant in front of our potential should be multiplied by n −4 . In Section 4 we will show that this also follows from our construction

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The ground state of the D = 11 supermembrane and matrix models on compact regions

Cited by 8 publications

References 43 publications

Measure of the potential valleys of the supermembrane theory

Measure of the potential valleys of the supermembrane theory

Classification of M2-brane 2-torus bundles, U -duality invariance, and type II gauged supergravities

Optimized Fock space in the large N limit of quartic interactions in matrix models

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