State-of-the-art in artificial neural network applications: A survey

Progress in particle and nuclear physics

These are notes based on a series of lectures given at the KITP workshop Quantum Criticality and the AdS/CFT Correspondence in July, 2009. The goal of the lectures was to introduce condensed matter physicists to the AdS/CFT correspondence. Discussion of string theory and of supersymmetry is avoided to the extent possible.

Holographic Duality with a View Toward Many-Body Physics

https://scholarworks.wm.edu/cgi/viewcontent.cgi?article=1956&context=aspubs

Light-front holographic QCD and emerging confinement

In this report we explore the remarkable connections between light-front dynamics, its holographic mapping to gravity in a higher-dimensional anti-de Sitter (AdS) space, and conformal quantum mechanics. This approach provides new insights into the origin of a fundamental mass scale and the physics underlying confinement dynamics in QCD in the limit of massless quarks. The result is a relativistic light-front wave equation for arbitrary spin with an effective confinement potential derived from a conformal action and its embedding in AdS space. This equation allows for the computation of essential features of hadron spectra in terms of a single scale. The light-front holographic methods described here gives a precise interpretation of holographic variables and quantities in AdS in terms of light-front variables and quantum numbers. This leads to a relation between the AdS wave functions and the boost-invariant light-front wave functions describing the internal structure of hadronic bound states in physical space-time. The pion is massless in the chiral limit and the excitation spectra of relativistic light-quark meson and baryon bound states lie on linear Regge trajectories with identical slopes in the radial and orbital quantum numbers. In the light-front holographic approach described here currents are expressed as an infinite sum of poles, and form factors as a product of poles. At large $q^2$ the form factor incorporates the correct power-law fall-off for hard scattering independent of the specific dynamics and is dictated by the twist. At low $q^2$ the form factor leads to vector dominance. The approach is also extended to include small quark masses. We briefly review in this report other holographic approaches to QCD, in particular top-down and bottom-up models based on chiral symmetry breaking. We also include a discussion of open problems and future applications.

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Light-Front Holographic QCD and Emerging Confinement

At the dawn of a new theoretical tool based on the AdS/CFT correspondence for nonperturbative aspects of quantum chromodynamics, we give an interim review on the new tool, holographic QCD, with some of its accomplishment. We try to give an A-to-Z picture of the holographic QCD, from string theory to a few selected top-down holographic QCD models with one or two physical applications in each model. We may not attempt to collect diverse results from various holographic QCD model studies.

Holographic QCD: Past, Present, and Future

Holographic QCD: Past, present, and future

Ab initio approaches in nuclear theory, such as the no-core shell model (NCSM), have been developed for approximately solving finite nuclei with realistic strong interactions. The NCSM and other approaches require an extrapolation of the results obtained in a finite basis space to the infinite basis space limit and assessment of the uncertainty of those extrapolations. Each observable requires a separate extrapolation and many observables have no proven extrapolation method. We propose a feed-forward artificial neural network (ANN) method as an extrapolation tool to obtain the ground-state energy and the ground-state point-proton root-mean-square (rms) radius along with their extrapolation uncertainties. The designed ANNs are sufficient to produce results for these two very different observables in $^{6}\mathrm{Li}$ from the ab initio NCSM results in small basis spaces that satisfy the following theoretical physics condition: independence of basis space parameters in the limit of extremely large matrices. Comparisons of the ANN results with other extrapolation methods are also provided.

Deep learning: Extrapolation tool for ab initio nuclear theory

We solve for properties of Li-6 in the ab initio no-core full configuration (NCFC) approach and we separately solve for its ground state and J(pi) = 2(2)(+) resonance with the Gamow shell model (GSM) in the Berggren basis. We employ both the JISP16 and chiral NNLOopt realistic nucleon-nucleon interactions and investigate the ground state energy, excitation energies, point proton root mean square (rms) radius and a suite of electroweak observables. We also extend and test methods to extrapolate the ground state energy, point proton rms radius, and electric quadrupole moment. We attain improved estimates of these observables in the NCFC approach by using basis spaces up through N-max = 18 that enable more definitive comparisons with experiment. Using the density matrix renormalization group approach with the JISP16 interaction, we find that we can significantly improve the convergence of the GSM treatment of the Li-6 ground state and J(pi) = 2(2)(+) resonance by adopting a natural orbital single-particle basis.

Ab initio no-core solutions for Li-6

We solve for properties of $^6$Li in the ab initio No-Core Full Configuration approach and we separately solve for its ground state and $J^{\pi}=2_{2}^{+}$ resonance with the Gamow Shell Model in the Berggren basis. We employ both the JISP16 and chiral NNLO$_{opt}$ realistic nucleon-nucleon interactions and investigate the ground state energy, excitation energies, point proton root-mean-square radius and a suite of electroweak observables. We also extend and test methods to extrapolate the ground state energy, point proton root-mean-square radius, and electric quadrupole moment. We attain improved estimates of these observables in the No-Core Full Configuration approach by using basis spaces up through N$_{max}$=18 that enable more definitive comparisons with experiment. Using the Density Matrix Renormalization Group approach with the JISP16 interaction, we find that we can significantly improve the convergence of the Gamow Shell Model treatment of the $^6$Li ground state and $J^{\pi}=2_{2}^{+}$ resonance by adopting a natural orbital single-particle basis.

Ik Jae Shin

Papers

Holographic QCD: Past, Present, and Future

Holographic QCD: Past, present, and future

Deep learning: Extrapolation tool for ab initio nuclear theory

Ab initio no-core solutions for Li-6

Ab initio no-core solutions for $^6$Li