The Experts below are selected from a list of 1698 Experts worldwide ranked by ideXlab platform
Makoto Sakamoto - One of the best experts on this subject based on the ideXlab platform.
-
A lattice formulation of N=2 supersymmetric SYK model
arXiv: High Energy Physics - Theory, 2018Co-Authors: Mitsuhiro Kato, Makoto SakamotoAbstract:We construct N=2 supersymmetric SYK model on one-dimensional (euclidean time) lattice. One nilpotent supersymmetry is exactly realized on the lattice in use of the cyclic Leibniz Rule (CLR).
-
Non-renormalization theorem in a lattice supersymmetric theory and the cyclic Leibniz Rule
Progress of Theoretical and Experimental Physics, 2017Co-Authors: Mitsuhiro Kato, Makoto SakamotoAbstract:N=4 supersymmetric quantum mechanical model is formulated on the lattice. Two supercharges, among four, are exactly conserved with the help of the cyclic Leibniz Rule without spoiling the locality. In use of the cohomological argument, any possible local terms of the effective action are classified into two categories which we call type-I and type-II, analogous to the D- and F-terms in the supersymmetric field theories. We prove non-renormalization theorem on the type-II terms which include mass and interaction terms with keeping a lattice constant finite, while type-I terms such as the kinetic terms have nontrivial quantum corrections.
-
Non-renormalization theorem and cyclic Leibniz Rule in lattice supersymmetry
Proceedings of The 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014), 2015Co-Authors: Mitsuhiro Kato, Makoto SakamotoAbstract:We propose a lattice model of supersymmetric complex quantum mechanics which realizes the non-renormalization theorem on a lattice. In our lattice model, the Leibniz Rule in the continuum, which cannot hold on a lattice due to a no-go theorem, is replaced by the cyclic Leibniz Rule (CLR) for difference operators. It is shown that CLR allows two of four supercharges of the continuum theory to preserve while a naive lattice model can realize one supercharge at the most. A striking feature of our lattice model is that there are no quantum corrections to potential terms in any finite order of perturbation theory. This is one of characteristic properties of supersymmetric theories in the continuum. It turns out that CLR plays a crucial role in the proof of the non-renormalization theorem. This result suggests that CLR grasps an essence of supersymmetry on a lattice.
-
Cyclic Leibniz Rule: a formulation of supersymmetry on lattice
Proceedings of 31st International Symposium on Lattice Field Theory LATTICE 2013 — PoS(LATTICE 2013), 2014Co-Authors: Mitsuhiro Kato, Makoto SakamotoAbstract:Department of Physics, Ehime University, Bunkyou-chou 2-5, Matsuyama 790-8577, JapanE-mail:so@phys.sci.ehime-u.ac.jpFor the purpose of constructing supersymmetric(SUSY) theories on lattice, we propose a newtype relation on lattice -cyclic Leibniz Rule(CLR)- which is slightly different from an ordinaryLeibniz Rule. Actually, we find that CLR can enlarge the numbe r of SUSYs and construct moreNicolai mappings in a quantum-mechanical model. In this model, the exact mass degeneracybetween fermion and boson is shown.31st International Symposium on Lattice Field Theory LATTICE 2013July 29 - August 3, 2013Mainz, Germany
-
Cyclic Leibniz Rule: a formulation of supersymmetry on lattice
arXiv: High Energy Physics - Lattice, 2013Co-Authors: Mitsuhiro Kato, Makoto SakamotoAbstract:For the purpose of constructing supersymmetric(SUSY) theories on lattice, we propose a new type relation on lattice -cyclic Leibniz Rule(CLR)- which is slightly different from an ordinary Leibniz Rule. Actually, we find that CLR can enlarge the number of SUSYs and construct more Nicolai mappings in a quantum-mechanical model. In this model, the exact mass degeneracy between fermion and boson is shown.
Mitsuhiro Kato - One of the best experts on this subject based on the ideXlab platform.
-
A lattice formulation of N=2 supersymmetric SYK model
arXiv: High Energy Physics - Theory, 2018Co-Authors: Mitsuhiro Kato, Makoto SakamotoAbstract:We construct N=2 supersymmetric SYK model on one-dimensional (euclidean time) lattice. One nilpotent supersymmetry is exactly realized on the lattice in use of the cyclic Leibniz Rule (CLR).
-
Non-renormalization theorem in a lattice supersymmetric theory and the cyclic Leibniz Rule
Progress of Theoretical and Experimental Physics, 2017Co-Authors: Mitsuhiro Kato, Makoto SakamotoAbstract:N=4 supersymmetric quantum mechanical model is formulated on the lattice. Two supercharges, among four, are exactly conserved with the help of the cyclic Leibniz Rule without spoiling the locality. In use of the cohomological argument, any possible local terms of the effective action are classified into two categories which we call type-I and type-II, analogous to the D- and F-terms in the supersymmetric field theories. We prove non-renormalization theorem on the type-II terms which include mass and interaction terms with keeping a lattice constant finite, while type-I terms such as the kinetic terms have nontrivial quantum corrections.
-
Non-renormalization theorem and cyclic Leibniz Rule in lattice supersymmetry
Proceedings of The 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014), 2015Co-Authors: Mitsuhiro Kato, Makoto SakamotoAbstract:We propose a lattice model of supersymmetric complex quantum mechanics which realizes the non-renormalization theorem on a lattice. In our lattice model, the Leibniz Rule in the continuum, which cannot hold on a lattice due to a no-go theorem, is replaced by the cyclic Leibniz Rule (CLR) for difference operators. It is shown that CLR allows two of four supercharges of the continuum theory to preserve while a naive lattice model can realize one supercharge at the most. A striking feature of our lattice model is that there are no quantum corrections to potential terms in any finite order of perturbation theory. This is one of characteristic properties of supersymmetric theories in the continuum. It turns out that CLR plays a crucial role in the proof of the non-renormalization theorem. This result suggests that CLR grasps an essence of supersymmetry on a lattice.
-
Cyclic Leibniz Rule: a formulation of supersymmetry on lattice
Proceedings of 31st International Symposium on Lattice Field Theory LATTICE 2013 — PoS(LATTICE 2013), 2014Co-Authors: Mitsuhiro Kato, Makoto SakamotoAbstract:Department of Physics, Ehime University, Bunkyou-chou 2-5, Matsuyama 790-8577, JapanE-mail:so@phys.sci.ehime-u.ac.jpFor the purpose of constructing supersymmetric(SUSY) theories on lattice, we propose a newtype relation on lattice -cyclic Leibniz Rule(CLR)- which is slightly different from an ordinaryLeibniz Rule. Actually, we find that CLR can enlarge the numbe r of SUSYs and construct moreNicolai mappings in a quantum-mechanical model. In this model, the exact mass degeneracybetween fermion and boson is shown.31st International Symposium on Lattice Field Theory LATTICE 2013July 29 - August 3, 2013Mainz, Germany
-
Cyclic Leibniz Rule: a formulation of supersymmetry on lattice
arXiv: High Energy Physics - Lattice, 2013Co-Authors: Mitsuhiro Kato, Makoto SakamotoAbstract:For the purpose of constructing supersymmetric(SUSY) theories on lattice, we propose a new type relation on lattice -cyclic Leibniz Rule(CLR)- which is slightly different from an ordinary Leibniz Rule. Actually, we find that CLR can enlarge the number of SUSYs and construct more Nicolai mappings in a quantum-mechanical model. In this model, the exact mass degeneracy between fermion and boson is shown.
So Hiroto - One of the best experts on this subject based on the ideXlab platform.
-
Numerical analyses of N=2 supersymmetric quantum mechanics with cyclic Leibniz Rule on lattice
'Oxford University Press (OUP)', 2019Co-Authors: Kadoh Daisuke, Kamei Takeru, So HirotoAbstract:We study a cyclic Leibniz Rule, which provides a systematic approach to lattice supersymmetry, using a numerical method with a transfer matrix. The computation is carried out in N=2 supersymmetric quantum mechanics with the phi^6-interaction for weak and strong couplings. The computed energy spectra and supersymmetric Ward-Takahashi identities are compared with those obtained from another lattice action. We find that a model with the cyclic Leibniz Rule behaves similarly to the continuum theory compared with the other lattice action.Comment: 37 pages, 12 figures and 8 table
-
A lattice formulation of the N=2 supersymmetric SYK model
'Oxford University Press (OUP)', 2018Co-Authors: Kato Mitsuhiro, Sakamoto Makoto, So HirotoAbstract:We construct the N=2 supersymmetric SYK model on a 1D (Euclidean time) lattice. One nilpotent supersymmetry is exactly realized on the lattice in the use of the cyclic Leibniz Rule
-
A lattice formulation of N=2 supersymmetric SYK model
'Oxford University Press (OUP)', 2018Co-Authors: Kato Mitsuhiro, Sakamoto Makoto, So HirotoAbstract:We construct N=2 supersymmetric SYK model on one-dimensional (euclidean time) lattice. One nilpotent supersymmetry is exactly realized on the lattice in use of the cyclic Leibniz Rule (CLR).Comment: 7 pages, letter; (v2) revised version to be published in PTE
De Oliveira E. Capelas - One of the best experts on this subject based on the ideXlab platform.
-
Leibniz type Rule: $\Psi-$Hilfer fractional derivative
2018Co-Authors: Sousa, Vanterler J. Da C., De Oliveira E. CapelasAbstract:In this paper, we present the Leibniz Rule for the $\Psi-$Hilfer ($\Psi-$H) fractional derivative in two versions, the first in relation to $\Psi-$RL fractional derivative and the second in relation to the $\Psi-$H fractional derivative. In this sense, we present some particular cases of Leibniz Rules and Leibniz type Rules from the investigated case.Comment: 16 page
E. Capelas De Oliveira - One of the best experts on this subject based on the ideXlab platform.
-
Leibniz type Rule: $\Psi-$Hilfer fractional derivative
arXiv: Classical Analysis and ODEs, 2018Co-Authors: J. Vanterler Da C. Sousa, E. Capelas De OliveiraAbstract:In this paper, we present the Leibniz Rule for the $\Psi-$Hilfer ($\Psi-$H) fractional derivative in two versions, the first in relation to $\Psi-$RL fractional derivative and the second in relation to the $\Psi-$H fractional derivative. In this sense, we present some particular cases of Leibniz Rules and Leibniz type Rules from the investigated case.
