99.9...% of the SU(2) BFSS ground state

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1. Très proche Cité par cet article Utilisé en profondeur par cet article Pas pertinent

   On the ground state wave function of matrix theory

   Ying-Hsuan Lin, Yin Xi · 2014 · Journal of High Energy Physics · cité 21 fois · Pas encore résumé

   Résumé scientifique

   A bstractWe propose an explicit construction of the leading terms in the asymptotic expansion of the ground state wave function of BFSS SU(N ) matrix quantum mechanics. Our proposal is consistent with the expected factorization property in various limits of the Coulomb branch, and involves a different scaling behavior from previous suggestions. We comment on some possible physical implications.

2. Proche Cité par cet article Pas pertinent

   Asymptotic Search for Ground States of SU(2) Matrix Theory

   M. B. Halpern, C. Schwartz · 1997 · International Journal of Modern Physics A · cité 65 fois · Pas encore résumé

   Résumé scientifique

   We introduce a complete set of gauge-invariant variables and a generalized Born–Oppenheimer formulation to search for normalizable zero-energy asymptotic solutions of the Schrodinger equation of SU(2) matrix theory. The asymptotic method gives only ground state candidates, which must be further tested for global stability. Our results include a set of such ground state candidates, including one state which is a singlet under spin (9).

3. Proche Cité par cet article Pas pertinent

   Asymptotic Ground State for 10 Dimensional Reduced Supersymmetric SU(2) Yang Mills Theory

   G. M. Graf, J. Hoppe · 1998 · arXiv: High Energy Physics - Theory · preprint, non relu par les pairs · cité 14 fois · Pas encore résumé

   Résumé scientifique

   We calculate the power law decay, and asymptotic form of a (unique) SO(9) and SU(2) invariant wave function satisfying, to leading and sub-leading order, $Q_{\hat{\beta}} \psi = 0$ for all 16 supercharges of the matrix model corresponding to supermembranes in 11 space-time dimensions.

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   Towards the Ground State of the Supermembrane

   Y. Michishita, M. Trzetrzelewski · 2012 · Nuclear Physics · cité 10 fois · Pas encore résumé

   Résumé scientifique

   The explicit, near the origin, form of the ground state of the SU(2) supermembrane matrix model is studied. We evaluate the 2nd order terms of the Taylor expansion of the wave-function, which together with the 0th and the 1st order terms can be used to determine other terms by recurrence equations coming from �

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   Asymptotic Factorisation of the Ground-State for SU(N)-invariant Supersymmetric Matrix-Models

   D. Hasler, J. Hoppe · 2002 · arXiv: High Energy Physics - Theory · preprint, non relu par les pairs · cité 18 fois · Pas encore résumé

   Résumé scientifique

   We give a simple - straightforward and rigorous - derivation that when the eigenvalues of one of the d = 9 (5,3,2) matrices in the SU(N) invariant supersymmetric matrix model become large (and well separated from each other) the ground-state wavefunction (resp. asymptotic zero-energy solution of the corresponding differential equation) factorizes, for all N > 1, into a product of supersymmetric harmonic oscillator wavefunctions (involving the ‘off-diagonal’ degrees of freedom) and a wavefunction that is annihilated by the free supercharge formed out of all ‘diagonal’ (Cartan sub-algebra) degrees of freedom. During the past few years, zero-energy states in supersymmetric matrix-models have be…

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   Construction of the zero-energy state of SU(2)-matrix theory: Near the origin

   J. Hoppe, D. Lundholm, M. Trzetrzelewski · 2008 · Nuclear Physics · cité 19 fois · Pas encore résumé

   Résumé scientifique

   We explicitly construct a (unique) Spin(9) x SU(2) singlet state, phi, involving only the fermionic degrees of freedom of the supersymmetric matrix-model corresponding to reduced 10-dimensional sup ...

7. Proche Cité par cet article Pas pertinent

   On asymptotic hamiltonian for SU(N) matrix theory

   A. Konechny · 1998 · Journal of High Energy Physics · cité 24 fois · Pas encore résumé

   Résumé scientifique

   We compute the leading contribution to the effective Hamiltonian of SU(N) matrix theory in the limit of large separation. We work with a gauge fixed Hamiltonian and use generalized Born-Oppenheimer approximation, extending the recent work of Halpern and Schwartz for SU(2) [8]. The answer turns out to be a free Hamiltonian for the coordinates along the flat directions of the potential. Applications to finding ground state candidates and calculation of the correction (surface) term to Witten index are discussed.

8. Proche Pas pertinent

   Uniqueness, Nondegeneracy, and Asymptotic Expansions of Ground States for the Dirac-Coulomb System

   Pan Chen, Qi Guo, Xiao-Yu Zeng · 2026 · Pas encore résumé

   Résumé scientifique

   We study ground states of the following Dirac-Coulomb system $$\mathscr{D}_cu_c- \left(\abs{x}^{-1}\ast \abs{u_c}^2\right)u_c=\omega_cu_c,$$ under the constraint $\norm[L^2]{u_c}^2=1.$For sufficiently large \(c\), we prove uniqueness of ground states modulo translations, phase transformations and spinorial rotations, and determine the kernel of the linearized operator at ground state. We also obtain asymptotic expansions of ground state in the nonrelativistic limit regime.

Les travaux antérieurs sur lesquels il s’appuie

1. Apparenté Pas pertinent

   Witten index and threshold bound states of D-branes

   Piljin Yi · 1997 · Nuclear Physics · cité 166 fois · Pas encore résumé

   Résumé scientifique

   We consider the Witten index I = Tr(−1)F of SU(2) super Yang-Mills quantum mechanics (SYMQ) with N = 16, 8, 4 supersymmetries. The theory governs the interactions between a pair of D-branes under various circumstances, and our goal is to count the number of the threshold bound states directly from the low-energy effective theory. String theory and M-theory have predicted that I = 1 for N = 16, which in fact forms an underlying hypothesis of the M(atrix)-theory formulation. Also the consistency of conifold transitions in type II theories is known to require I = 0 for N = 8 and 4. Here, the bulk contribution to I is computed explicitly, and for N = 16, 8, 4, found to be 54, 14, 14 respectively…

2. Apparenté Pas pertinent

   Bound states at threshold in supersymmetric quantum mechanics

   Massimo Porrati, A. Rozenberg · 1997 · Nuclear Physics · cité 91 fois · Pas encore résumé

   Résumé scientifique

   Abstract We propose a general method that allows the detection of the existence of normalizable ground states in supersymmetric quantum mechanical systems with a non-Fredholm spectrum. We apply our method to show the existence of bound states at threshold in two important cases: (i) the quantum mechanical system describing H-monopoles; (ii) the quantum mechanics of D0 branes.

3. Apparenté Pas pertinent

   Bootstrap bounds on D0-brane quantum mechanics

   Henry W. Lin · 2023 · Journal of High Energy Physics · cité 38 fois · Pas encore résumé

   Résumé scientifique

   We derive simple bootstrap bounds on correlation functions of the BFSS matrix theory/D0-brane quantum mechanics. The result strengthens and extends Polchinski’s virial theorem bound to finite energies and gives the first non-trivial bound on ⟨Tr X2⟩. Despite their simplicity, the bounds hint at some features of the dual black hole geometry. Our best lower bounds are already a factor of ∼ 2 from existing Monte Carlo results.

4. Apparenté Pas pertinent

   Hamiltonian truncation study of supersymmetric quantum mechanics: S-matrix and metastable states

   Bruno Balthazar, V. Rodríguez, Xi Yin · 2016 · Journal of High Energy Physics · cité 7 fois · Pas encore résumé

   Résumé scientifique

   We implement the Rayleigh-Ritz method in supersymmetric quantum mechanics with flat directions, and extract the S-matrix and metastable resonances. The effectiveness of the method is demonstrated in two strongly coupled systems: an N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 1 toy supermembrane model, and an N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{u…

5. Apparenté Pas pertinent

   Normalized vacuum states in N=4 supersymmetric Yang–Mills quantum mechanics with any gauge group

   V. Kac, A. Smilga · 1999 · Nuclear Physics · cité 72 fois · Pas encore résumé

   Résumé scientifique

   Abstract We study the question of existence and the number of normalized vacuum states in N =4 super-Yang–Mills quantum mechanics for any gauge group. The mass deformation method is the simplest and clearest one. It allowed us to calculate the number of normalized vacuum states for all gauge groups. For all unitary groups, #vac=1, but for the symplectic groups [starting from Sp(6) ], for the orthogonal groups [starting from SO(8)] and for all the exceptional groups, it is greater than one. We also discuss at length the functional integral method. We calculate the “deficit term” for some non-unitary groups and predict the value of the integral giving the “principal contribution”. The issues l…