Measure of the potential valleys of the supermembrane theory

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

doi:10.1016/j.physletb.2019.134873

Cited by 3 publications

(3 citation statements)

References 19 publications

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“…iii) The embedding H 1 (K) ⊂ L 2 (K) is compact according to know results in [36]. All this is in agreement with the previous findings of [32,33,34].…”

Section: Discussionsupporting

confidence: 90%

Existence of a Supersymmetric Massless Ground State of the $SU(N)$ Matrix Model globally on its Valleys

Boulton,

del Moral,

Restuccia

2021

Preprint

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In this work we consider the existence and uniqueness of the ground state of the regularized Hamiltonian of the Supermembrane in dimensions D = 4, 5, 7 and 11, or equivalently the SU (N ) Matrix Model. That is, the 0+1 reduction of the 10dimensional SU (N ) Super Yang-Mills Hamiltonian. This ground state problem is associated with the solutions of the inner and outer Dirichlet problems for this operator, and their subsequent smooth patching (glueing) into a single state. We have discussed properties of the inner problem in a previous work, therefore we now investigate the outer Dirichlet problem for the Hamiltonian operator. We establish existence and uniqueness on unbounded valleys defined in terms of the bosonic potential. These are precisely those regions where the bosonic part of the potential is less than a given value V 0 , which we set to be arbitrary. The problem is well posed, since these valleys are preserved by the action of the SU (N ) constraint. We first show that their Lebesgue measure is finite, subject to restrictions on D in terms of N . We then use this analysis to determine a bound on the fermionic potential which yields the coercive property of the energy form. It is from this, that we derive the existence and uniqueness of the solution. As a by-product of our argumentation, we show that the Hamiltonian, restricted to the valleys, has spectrum purely discrete with finite multiplicity. Remarkably, this is in contrast to the case of the unrestricted space, where it is well known that the spectrum comprises a continuous segment. We discuss the relation of our work with the general ground state problem and the question of confinement in models with strong interactions.

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“…iii) The embedding H 1 (K) ⊂ L 2 (K) is compact according to know results in [36]. All this is in agreement with the previous findings of [32,33,34].…”

Section: Discussionsupporting

confidence: 90%

Existence of a Supersymmetric Massless Ground State of the $SU(N)$ Matrix Model globally on its Valleys

Boulton,

del Moral,

Restuccia

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…ii) The fermionic potential satisfies a crucial estimate (see section 4), which renders a coercive Hamiltonian. iii) The embedding H 1 (K) ⊂ L 2 (K) is compact according to know results in [40]. All this is in agreement with the previous findings of [35][36][37].…”

Section: Discussionsupporting

confidence: 90%

“…Hence Q( Ψ) = Q † ( Ψ) = 0. Thus, from lemma 1 of [40], Ψ = 0. This is clearly a contradiction.…”

Section: Lemmamentioning

confidence: 92%

Existence of a supersymmetric massless ground state of the SU(N) matrix model globally on its valleys

Boulton

Moral

Restuccia

2021

J. High Energ. Phys.

Self Cite

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In this work we consider the existence and uniqueness of the ground state of the regularized Hamiltonian of the Supermembrane in dimensions D = 4, 5, 7 and 11, or equivalently the SU(N) Matrix Model. That is, the 0+1 reduction of the 10-dimensional SU(N) Super Yang-Mills Hamiltonian. This ground state problem is associated with the solutions of the inner and outer Dirichlet problems for this operator, and their subsequent smooth patching (glueing) into a single state. We have discussed properties of the inner problem in a previous work, therefore we now investigate the outer Dirichlet problem for the Hamiltonian operator. We establish existence and uniqueness on unbounded valleys defined in terms of the bosonic potential. These are precisely those regions where the bosonic part of the potential is less than a given value V0, which we set to be arbitrary. The problem is well posed, since these valleys are preserved by the action of the SU(N) constraint. We first show that their Lebesgue measure is finite, subject to restrictions on D in terms of N. We then use this analysis to determine a bound on the fermionic potential which yields the coercive property of the energy form. It is from this, that we derive the existence and uniqueness of the solution. As a by-product of our argumentation, we show that the Hamiltonian, restricted to the valleys, has spectrum purely discrete with finite multiplicity. Remarkably, this is in contrast to the case of the unrestricted space, where it is well known that the spectrum comprises a continuous segment. We discuss the relation of our work with the general ground state problem and the question of confinement in models with strong interactions.

show abstract

Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams

Sati

Schreiber

2022

Advances in Theoretical and Mathematical Physics

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Measure of the potential valleys of the supermembrane theory

Cited by 3 publications

References 19 publications

Existence of a Supersymmetric Massless Ground State of the $SU(N)$ Matrix Model globally on its Valleys

Existence of a Supersymmetric Massless Ground State of the $SU(N)$ Matrix Model globally on its Valleys

Existence of a supersymmetric massless ground state of the SU(N) matrix model globally on its valleys

Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams

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